Establishment of gravitational head in 1D

These tests concern the steady-state pressure distribution obtained either by running a transient model for a long time, or by running a steady-state analysis, both of which should lead to the same result.

Without fluxes, the steadystate pressure distribution is just $var element = document.getElementById("moose-equation-6f0a2c97-d151-47a5-8886-5f3bb8577298");katex.render("P(x) = P_{0} - \\rho_{0} g x \\ ,", element, {displayMode:true,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ if the fluid bulk modulus, $var element = document.getElementById("moose-equation-1ba0113d-5a1f-47e9-a239-86a0dd750574");katex.render("B", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ , is large enough compared with $var element = document.getElementById("moose-equation-fd362eae-b8e4-4f0f-8e19-5fd71f690079");katex.render("P", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ . Here $var element = document.getElementById("moose-equation-494677f2-6ba0-4d69-8e70-4277aadfade0");katex.render("P_{0}", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ is the porepressure at $var element = document.getElementById("moose-equation-3343ba59-5df6-49cd-adcd-464e3c7191fc");katex.render("x=0", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ . For smaller bulk modulus $(1)var element = document.getElementById("moose-equation-79c80346-e2bb-405f-a90d-ae640dc23091");katex.render("P(x) = -B \\log\\left( e^{-P_{0}/B} + \\frac{g\\rho_{0}x}{B} \\right) \\ . ", element, {displayMode:true,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ Here it is assumed that the density is given by $var element = document.getElementById("moose-equation-efac688b-03f4-4200-a391-4ec297a03fec");katex.render("\\rho = \\rho_{0}e^{-P/B}", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ with constant bulk modulus, $var element = document.getElementById("moose-equation-f81155a8-58c6-45af-9b73-6bde3d19b5b3");katex.render("g", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ is the magnitude acceleration due to gravity (a vector assumed to be pointing in the negative $var element = document.getElementById("moose-equation-65ee6113-c436-4426-afc9-bd6736117c63");katex.render("x", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ direction), and $var element = document.getElementById("moose-equation-863aa479-4cd1-4963-beb1-c5d6a4eff8a2");katex.render("x", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ is position. The tests described below are simple tests and are part of the automatic test suite.

Single-phase, single-component

Two single-phase simulations with 100 1D elements are run: one with fully-saturated conditions, and the other with unsaturated conditions using the van Genuchten capillary pressure (this should not, and does not, make any difference to the results). The porepressure is held fixed at one boundary ( $var element = document.getElementById("moose-equation-076ff710-31fc-4e79-bbae-4c976416ef41");katex.render("x=0", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ ). The parameters are tabulated in Table 1.

Table 1: Parameter values used in the 1-phase tests

Parameter	Value
x	$var element = document.getElementById("moose-equation-3734649e-1c12-4238-b167-9808c703a272");katex.render("-1\\leq x \\leq 0\\,", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ m
Bulk modulus (B)	1.2 Pa
Reference density $var element = document.getElementById("moose-equation-dd887ddb-f30f-4e29-8a49-837651a6905a");katex.render("\\rho_{0}", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$	1 kg.m $var element = document.getElementById("moose-equation-2f356d5f-3168-4a93-9da0-e4aadc89b2fc");katex.render("^{-3}", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$
gravitational acceleration $var element = document.getElementById("moose-equation-4ee1f2e7-b0ba-4f92-a940-1fb2227c5095");katex.render("g", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$	-1 m.s $var element = document.getElementById("moose-equation-a14bb000-fec3-4ff5-850e-51e51ea97384");katex.render("^{-2}", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$

The steady-state input file with full saturation:

# Checking that gravity head is established
# 1phase, vanGenuchten, constant fluid-bulk, constant viscosity, constant permeability, Corey relative perm
# fully saturated
# For better agreement with the analytical solution (ana_pp), just increase nx

[Mesh<<<{"href": "../../../../syntax/Mesh/index.html"}>>>]
  type = GeneratedMesh
  dim = 1
  nx = 100
  xmin = -1
  xmax = 0
[]

[GlobalParams<<<{"href": "../../../../syntax/GlobalParams/index.html"}>>>]
  PorousFlowDictator = dictator
[]

[Variables<<<{"href": "../../../../syntax/Variables/index.html"}>>>]
  [pp]
    [InitialCondition]
      type = RandomIC
      min = 0
      max = 1
    []
  []
[]

[Kernels<<<{"href": "../../../../syntax/Kernels/index.html"}>>>]
  [flux0]
    type = PorousFlowAdvectiveFlux<<<{"description": "Fully-upwinded advective flux of the component given by fluid_component", "href": "../../../../source/kernels/PorousFlowAdvectiveFlux.html"}>>>
    fluid_component<<<{"description": "The index corresponding to the fluid component for this kernel"}>>> = 0
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = pp
    gravity<<<{"description": "Gravitational acceleration vector downwards (m/s^2)"}>>> = '-1 0 0'
  []
[]

[Functions<<<{"href": "../../../../syntax/Functions/index.html"}>>>]
  [ana_pp]
    type = ParsedFunction<<<{"description": "Function created by parsing a string", "href": "../../../../source/functions/MooseParsedFunction.html"}>>>
    symbol_names<<<{"description": "Symbols (excluding t,x,y,z) that are bound to the values provided by the corresponding items in the vals vector."}>>> = 'g B p0 rho0'
    symbol_values<<<{"description": "Constant numeric values, postprocessor names, function names, and scalar variables corresponding to the symbols in symbol_names."}>>> = '1 1.2 0 1'
    expression<<<{"description": "The user defined function."}>>> = '-B*log(exp(-p0/B)+g*rho0*x/B)' # expected pp at base
  []
[]

[BCs<<<{"href": "../../../../syntax/BCs/index.html"}>>>]
  [z]
    type = DirichletBC<<<{"description": "Imposes the essential boundary condition $u=g$, where $g$ is a constant, controllable value.", "href": "../../../../source/bcs/DirichletBC.html"}>>>
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = pp
    boundary<<<{"description": "The list of boundary IDs from the mesh where this object applies"}>>> = right
    value<<<{"description": "Value of the BC"}>>> = 0
  []
[]

[UserObjects<<<{"href": "../../../../syntax/UserObjects/index.html"}>>>]
  [dictator]
    type = PorousFlowDictator<<<{"description": "Holds information on the PorousFlow variable names", "href": "../../../../source/userobjects/PorousFlowDictator.html"}>>>
    porous_flow_vars<<<{"description": "List of primary variables that are used in the PorousFlow simulation.  Jacobian entries involving derivatives wrt these variables will be computed.  In single-phase models you will just have one (eg 'pressure'), in two-phase models you will have two (eg 'p_water p_gas', or 'p_water s_water'), etc."}>>> = 'pp'
    number_fluid_phases<<<{"description": "The number of fluid phases in the simulation"}>>> = 1
    number_fluid_components<<<{"description": "The number of fluid components in the simulation"}>>> = 1
  []
  [pc]
    type = PorousFlowCapillaryPressureVG<<<{"description": "van Genuchten capillary pressure", "href": "../../../../source/userobjects/PorousFlowCapillaryPressureVG.html"}>>>
    m<<<{"description": "van Genuchten exponent m. Must be between 0 and 1, and optimally should be set to >0.5"}>>> = 0.5
    alpha<<<{"description": "van Genuchten parameter alpha. Must be positive"}>>> = 1
  []
[]

[FluidProperties<<<{"href": "../../../../syntax/FluidProperties/index.html"}>>>]
  [simple_fluid]
    type = SimpleFluidProperties<<<{"description": "Fluid properties for a simple fluid with a constant bulk density", "href": "../../../../source/fluidproperties/SimpleFluidProperties.html"}>>>
    bulk_modulus<<<{"description": "Constant bulk modulus (Pa)"}>>> = 1.2
    density0<<<{"description": "Density at zero pressure and zero temperature"}>>> = 1
    viscosity<<<{"description": "Constant dynamic viscosity (Pa.s)"}>>> = 1
    thermal_expansion<<<{"description": "Constant coefficient of thermal expansion (1/K)"}>>> = 0
  []
[]

[Materials<<<{"href": "../../../../syntax/Materials/index.html"}>>>]
  [temperature]
    type = PorousFlowTemperature<<<{"description": "Material to provide temperature at the quadpoints or nodes and derivatives of it with respect to the PorousFlow variables", "href": "../../../../source/materials/PorousFlowTemperature.html"}>>>
  []
  [ppss]
    type = PorousFlow1PhaseP<<<{"description": "This Material is used for the partially saturated single-phase situation where porepressure is the primary variable", "href": "../../../../source/materials/PorousFlow1PhaseP.html"}>>>
    porepressure<<<{"description": "Variable that represents the porepressure of the single phase"}>>> = pp
    capillary_pressure<<<{"description": "Name of the UserObject defining the capillary pressure"}>>> = pc
  []
  [massfrac]
    type = PorousFlowMassFraction<<<{"description": "This Material forms a std::vector<std::vector ...> of mass-fractions out of the individual mass fractions", "href": "../../../../source/materials/PorousFlowMassFraction.html"}>>>
  []
  [simple_fluid]
    type = PorousFlowSingleComponentFluid<<<{"description": "This Material calculates fluid properties at the quadpoints or nodes for a single component fluid", "href": "../../../../source/materials/PorousFlowSingleComponentFluid.html"}>>>
    fp<<<{"description": "The name of the user object for fluid properties"}>>> = simple_fluid
    phase<<<{"description": "The phase number"}>>> = 0
  []
  [permeability]
    type = PorousFlowPermeabilityConst<<<{"description": "This Material calculates the permeability tensor assuming it is constant", "href": "../../../../source/materials/PorousFlowPermeabilityConst.html"}>>>
    permeability<<<{"description": "The permeability tensor (usually in m^2), which is assumed constant for this material"}>>> = '1 0 0  0 2 0  0 0 3'
  []
  [relperm]
    type = PorousFlowRelativePermeabilityCorey<<<{"description": "This Material calculates relative permeability of the fluid phase, using the simple Corey model ((S-S_res)/(1-sum(S_res)))^n", "href": "../../../../source/materials/PorousFlowRelativePermeabilityCorey.html"}>>>
    n<<<{"description": "The Corey exponent of the phase."}>>> = 1
    phase<<<{"description": "The phase number"}>>> = 0
  []
[]

[Postprocessors<<<{"href": "../../../../syntax/Postprocessors/index.html"}>>>]
  [pp_base]
    type = PointValue<<<{"description": "Compute the value of a variable at a specified location", "href": "../../../../source/postprocessors/PointValue.html"}>>>
    variable<<<{"description": "The name of the variable that this postprocessor operates on."}>>> = pp
    point<<<{"description": "The physical point where the solution will be evaluated."}>>> = '-1 0 0'
  []
  [pp_analytical]
    type = FunctionValuePostprocessor<<<{"description": "Computes the value of a supplied function at a single point (scalable)", "href": "../../../../source/postprocessors/FunctionValuePostprocessor.html"}>>>
    function<<<{"description": "The function which supplies the postprocessor value."}>>> = ana_pp
    point<<<{"description": "A set of three PostprocessorNames or constant values (or any mixture thereof) that will be passed to the function in the space argument"}>>> = '-1 0 0'
  []
  [pp_00]
    type = PointValue<<<{"description": "Compute the value of a variable at a specified location", "href": "../../../../source/postprocessors/PointValue.html"}>>>
    variable<<<{"description": "The name of the variable that this postprocessor operates on."}>>> = pp
    point<<<{"description": "The physical point where the solution will be evaluated."}>>> = '0 0 0'
  []
  [pp_01]
    type = PointValue<<<{"description": "Compute the value of a variable at a specified location", "href": "../../../../source/postprocessors/PointValue.html"}>>>
    variable<<<{"description": "The name of the variable that this postprocessor operates on."}>>> = pp
    point<<<{"description": "The physical point where the solution will be evaluated."}>>> = '-0.1 0 0'
  []
  [pp_02]
    type = PointValue<<<{"description": "Compute the value of a variable at a specified location", "href": "../../../../source/postprocessors/PointValue.html"}>>>
    variable<<<{"description": "The name of the variable that this postprocessor operates on."}>>> = pp
    point<<<{"description": "The physical point where the solution will be evaluated."}>>> = '-0.2 0 0'
  []
  [pp_03]
    type = PointValue<<<{"description": "Compute the value of a variable at a specified location", "href": "../../../../source/postprocessors/PointValue.html"}>>>
    variable<<<{"description": "The name of the variable that this postprocessor operates on."}>>> = pp
    point<<<{"description": "The physical point where the solution will be evaluated."}>>> = '-0.3 0 0'
  []
  [pp_04]
    type = PointValue<<<{"description": "Compute the value of a variable at a specified location", "href": "../../../../source/postprocessors/PointValue.html"}>>>
    variable<<<{"description": "The name of the variable that this postprocessor operates on."}>>> = pp
    point<<<{"description": "The physical point where the solution will be evaluated."}>>> = '-0.4 0 0'
  []
  [pp_05]
    type = PointValue<<<{"description": "Compute the value of a variable at a specified location", "href": "../../../../source/postprocessors/PointValue.html"}>>>
    variable<<<{"description": "The name of the variable that this postprocessor operates on."}>>> = pp
    point<<<{"description": "The physical point where the solution will be evaluated."}>>> = '-0.5 0 0'
  []
  [pp_06]
    type = PointValue<<<{"description": "Compute the value of a variable at a specified location", "href": "../../../../source/postprocessors/PointValue.html"}>>>
    variable<<<{"description": "The name of the variable that this postprocessor operates on."}>>> = pp
    point<<<{"description": "The physical point where the solution will be evaluated."}>>> = '-0.6 0 0'
  []
  [pp_07]
    type = PointValue<<<{"description": "Compute the value of a variable at a specified location", "href": "../../../../source/postprocessors/PointValue.html"}>>>
    variable<<<{"description": "The name of the variable that this postprocessor operates on."}>>> = pp
    point<<<{"description": "The physical point where the solution will be evaluated."}>>> = '-0.7 0 0'
  []
  [pp_08]
    type = PointValue<<<{"description": "Compute the value of a variable at a specified location", "href": "../../../../source/postprocessors/PointValue.html"}>>>
    variable<<<{"description": "The name of the variable that this postprocessor operates on."}>>> = pp
    point<<<{"description": "The physical point where the solution will be evaluated."}>>> = '-0.8 0 0'
  []
  [pp_09]
    type = PointValue<<<{"description": "Compute the value of a variable at a specified location", "href": "../../../../source/postprocessors/PointValue.html"}>>>
    variable<<<{"description": "The name of the variable that this postprocessor operates on."}>>> = pp
    point<<<{"description": "The physical point where the solution will be evaluated."}>>> = '-0.9 0 0'
  []
  [pp_10]
    type = PointValue<<<{"description": "Compute the value of a variable at a specified location", "href": "../../../../source/postprocessors/PointValue.html"}>>>
    variable<<<{"description": "The name of the variable that this postprocessor operates on."}>>> = pp
    point<<<{"description": "The physical point where the solution will be evaluated."}>>> = '-1 0 0'
  []
[]

[Preconditioning<<<{"href": "../../../../syntax/Preconditioning/index.html"}>>>]
  [andy]
    type = SMP<<<{"description": "Single matrix preconditioner (SMP) builds a preconditioner using user defined off-diagonal parts of the Jacobian.", "href": "../../../../source/preconditioners/SingleMatrixPreconditioner.html"}>>>
    full<<<{"description": "Set to true if you want the full set of couplings between variables simply for convenience so you don't have to set every off_diag_row and off_diag_column combination."}>>> = true
  []
[]

[Executioner<<<{"href": "../../../../syntax/Executioner/index.html"}>>>]
  type = Steady
  solve_type = Newton
[]

[Outputs<<<{"href": "../../../../syntax/Outputs/index.html"}>>>]
  execute_on<<<{"description": "The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html."}>>> = 'timestep_end'
  file_base<<<{"description": "Common file base name to be utilized with all output objects"}>>> = grav01a
  [csv]
    type = CSV<<<{"description": "Output for postprocessors, vector postprocessors, and scalar variables using comma seperated values (CSV).", "href": "../../../../source/outputs/CSV.html"}>>>
  []
[]

The steady-state input file with partial saturation

# Checking that gravity head is established
# 1phase, vanGenuchten, constant fluid-bulk, constant viscosity, constant permeability, Corey relative perm
# unsaturated
# For better agreement with the analytical solution (ana_pp), just increase nx

[Mesh<<<{"href": "../../../../syntax/Mesh/index.html"}>>>]
  type = GeneratedMesh
  dim = 1
  nx = 100
  xmin = -1
  xmax = 0
[]

[GlobalParams<<<{"href": "../../../../syntax/GlobalParams/index.html"}>>>]
  PorousFlowDictator = dictator
[]

[Variables<<<{"href": "../../../../syntax/Variables/index.html"}>>>]
  [pp]
    [InitialCondition]
      type = RandomIC
      min = -1
      max = 1
    []
  []
[]

[Kernels<<<{"href": "../../../../syntax/Kernels/index.html"}>>>]
  [flux0]
    type = PorousFlowAdvectiveFlux<<<{"description": "Fully-upwinded advective flux of the component given by fluid_component", "href": "../../../../source/kernels/PorousFlowAdvectiveFlux.html"}>>>
    fluid_component<<<{"description": "The index corresponding to the fluid component for this kernel"}>>> = 0
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = pp
    gravity<<<{"description": "Gravitational acceleration vector downwards (m/s^2)"}>>> = '-1 0 0'
  []
[]

[Functions<<<{"href": "../../../../syntax/Functions/index.html"}>>>]
  [ana_pp]
    type = ParsedFunction<<<{"description": "Function created by parsing a string", "href": "../../../../source/functions/MooseParsedFunction.html"}>>>
    symbol_names<<<{"description": "Symbols (excluding t,x,y,z) that are bound to the values provided by the corresponding items in the vals vector."}>>> = 'g B p0 rho0'
    symbol_values<<<{"description": "Constant numeric values, postprocessor names, function names, and scalar variables corresponding to the symbols in symbol_names."}>>> = '1 2 -1 1'
    expression<<<{"description": "The user defined function."}>>> = '-B*log(exp(-p0/B)+g*rho0*x/B)' # expected pp at base
  []
[]

[BCs<<<{"href": "../../../../syntax/BCs/index.html"}>>>]
  [z]
    type = DirichletBC<<<{"description": "Imposes the essential boundary condition $u=g$, where $g$ is a constant, controllable value.", "href": "../../../../source/bcs/DirichletBC.html"}>>>
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = pp
    boundary<<<{"description": "The list of boundary IDs from the mesh where this object applies"}>>> = right
    value<<<{"description": "Value of the BC"}>>> = -1
  []
[]

[UserObjects<<<{"href": "../../../../syntax/UserObjects/index.html"}>>>]
  [dictator]
    type = PorousFlowDictator<<<{"description": "Holds information on the PorousFlow variable names", "href": "../../../../source/userobjects/PorousFlowDictator.html"}>>>
    porous_flow_vars<<<{"description": "List of primary variables that are used in the PorousFlow simulation.  Jacobian entries involving derivatives wrt these variables will be computed.  In single-phase models you will just have one (eg 'pressure'), in two-phase models you will have two (eg 'p_water p_gas', or 'p_water s_water'), etc."}>>> = 'pp'
    number_fluid_phases<<<{"description": "The number of fluid phases in the simulation"}>>> = 1
    number_fluid_components<<<{"description": "The number of fluid components in the simulation"}>>> = 1
  []
  [pc]
    type = PorousFlowCapillaryPressureVG<<<{"description": "van Genuchten capillary pressure", "href": "../../../../source/userobjects/PorousFlowCapillaryPressureVG.html"}>>>
    m<<<{"description": "van Genuchten exponent m. Must be between 0 and 1, and optimally should be set to >0.5"}>>> = 0.5
    alpha<<<{"description": "van Genuchten parameter alpha. Must be positive"}>>> = 1
  []
[]

[FluidProperties<<<{"href": "../../../../syntax/FluidProperties/index.html"}>>>]
  [simple_fluid]
    type = SimpleFluidProperties<<<{"description": "Fluid properties for a simple fluid with a constant bulk density", "href": "../../../../source/fluidproperties/SimpleFluidProperties.html"}>>>
    bulk_modulus<<<{"description": "Constant bulk modulus (Pa)"}>>> = 2
    density0<<<{"description": "Density at zero pressure and zero temperature"}>>> = 1
    viscosity<<<{"description": "Constant dynamic viscosity (Pa.s)"}>>> = 1
    thermal_expansion<<<{"description": "Constant coefficient of thermal expansion (1/K)"}>>> = 0
  []
[]

[Materials<<<{"href": "../../../../syntax/Materials/index.html"}>>>]
  [temperature]
    type = PorousFlowTemperature<<<{"description": "Material to provide temperature at the quadpoints or nodes and derivatives of it with respect to the PorousFlow variables", "href": "../../../../source/materials/PorousFlowTemperature.html"}>>>
  []
  [ppss]
    type = PorousFlow1PhaseP<<<{"description": "This Material is used for the partially saturated single-phase situation where porepressure is the primary variable", "href": "../../../../source/materials/PorousFlow1PhaseP.html"}>>>
    porepressure<<<{"description": "Variable that represents the porepressure of the single phase"}>>> = pp
    capillary_pressure<<<{"description": "Name of the UserObject defining the capillary pressure"}>>> = pc
  []
  [massfrac]
    type = PorousFlowMassFraction<<<{"description": "This Material forms a std::vector<std::vector ...> of mass-fractions out of the individual mass fractions", "href": "../../../../source/materials/PorousFlowMassFraction.html"}>>>
  []
  [simple_fluid]
    type = PorousFlowSingleComponentFluid<<<{"description": "This Material calculates fluid properties at the quadpoints or nodes for a single component fluid", "href": "../../../../source/materials/PorousFlowSingleComponentFluid.html"}>>>
    fp<<<{"description": "The name of the user object for fluid properties"}>>> = simple_fluid
    phase<<<{"description": "The phase number"}>>> = 0
  []
  [permeability]
    type = PorousFlowPermeabilityConst<<<{"description": "This Material calculates the permeability tensor assuming it is constant", "href": "../../../../source/materials/PorousFlowPermeabilityConst.html"}>>>
    permeability<<<{"description": "The permeability tensor (usually in m^2), which is assumed constant for this material"}>>> = '1 0 0  0 2 0  0 0 3'
  []
  [relperm]
    type = PorousFlowRelativePermeabilityCorey<<<{"description": "This Material calculates relative permeability of the fluid phase, using the simple Corey model ((S-S_res)/(1-sum(S_res)))^n", "href": "../../../../source/materials/PorousFlowRelativePermeabilityCorey.html"}>>>
    n<<<{"description": "The Corey exponent of the phase."}>>> = 1
    phase<<<{"description": "The phase number"}>>> = 0
  []
[]

[Postprocessors<<<{"href": "../../../../syntax/Postprocessors/index.html"}>>>]
  [pp_base]
    type = PointValue<<<{"description": "Compute the value of a variable at a specified location", "href": "../../../../source/postprocessors/PointValue.html"}>>>
    variable<<<{"description": "The name of the variable that this postprocessor operates on."}>>> = pp
    point<<<{"description": "The physical point where the solution will be evaluated."}>>> = '-1 0 0'
  []
  [pp_analytical]
    type = FunctionValuePostprocessor<<<{"description": "Computes the value of a supplied function at a single point (scalable)", "href": "../../../../source/postprocessors/FunctionValuePostprocessor.html"}>>>
    function<<<{"description": "The function which supplies the postprocessor value."}>>> = ana_pp
    point<<<{"description": "A set of three PostprocessorNames or constant values (or any mixture thereof) that will be passed to the function in the space argument"}>>> = '-1 0 0'
  []
[]

[Preconditioning<<<{"href": "../../../../syntax/Preconditioning/index.html"}>>>]
  [andy]
    type = SMP<<<{"description": "Single matrix preconditioner (SMP) builds a preconditioner using user defined off-diagonal parts of the Jacobian.", "href": "../../../../source/preconditioners/SingleMatrixPreconditioner.html"}>>>
    full<<<{"description": "Set to true if you want the full set of couplings between variables simply for convenience so you don't have to set every off_diag_row and off_diag_column combination."}>>> = true
  []
[]

[Executioner<<<{"href": "../../../../syntax/Executioner/index.html"}>>>]
  type = Steady
  solve_type = Newton
[]

[Outputs<<<{"href": "../../../../syntax/Outputs/index.html"}>>>]
  execute_on<<<{"description": "The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html."}>>> = 'timestep_end'
  file_base<<<{"description": "Common file base name to be utilized with all output objects"}>>> = grav01c
  exodus<<<{"description": "Output the results using the default settings for Exodus output."}>>> = true
  [csv]
    type = CSV<<<{"description": "Output for postprocessors, vector postprocessors, and scalar variables using comma seperated values (CSV).", "href": "../../../../source/outputs/CSV.html"}>>>
  []
[]

An example verification is shown in Figure 1, which also shows results from a 2-phase simulation (see next section)

Figure 1: Comparison between the MOOSE result (in dots), and the exact analytic expression given by Eq. (1).

Two-phase, two-component

Two-phase, two-component simulations may also be checked against Eq. (1). A number of simulations are performed with parameters tabulated in Table 2.

Table 2: Parameter values used in the 2-phase tests

Parameter	Value
x	$var element = document.getElementById("moose-equation-8ce4e920-f526-4710-9fe4-6440f6603acd");katex.render("-1\\leq x \\leq 0\\,", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ m
Bulk modulus of heavy phase	1.2 Pa
Bulk modulus of light phase	1 Pa
Reference density of heavy phase	1 kg.m $var element = document.getElementById("moose-equation-5431d30a-250a-4837-83c8-12fd4be6b72c");katex.render("^{-3}", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$
Reference density of light phase	0.1 kg.m $var element = document.getElementById("moose-equation-f6632e42-4965-47ec-b809-88d1996cac1d");katex.render("^{-3}", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$
gravitational acceleration $var element = document.getElementById("moose-equation-d9a7d9c8-ba11-41f9-8cbd-44173ccb4ad8");katex.render("g", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$	-1 m.s $var element = document.getElementById("moose-equation-49c2533b-e899-49ae-9bfe-a23a946ff631");katex.render("^{-2}", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$

One steady-state simulation is performed. Steady-state simulations are more difficult to perform in two-phase situations because of the inherently stronger nonlinearities, but mostly because simulations can easily enter unphysical domains (negative saturation, for instance) without the stabilising presence of the mass time-derivative. The steady-state input file:

# Checking that gravity head is established in the steady-state situation when 0<saturation<1 (note the strictly less-than).
# 2phase (PP), 2components, vanGenuchten, constant fluid bulk-moduli for each phase, constant viscosity, constant permeability, Corey relative perm
# For better agreement with the analytical solution (ana_pp), just increase nx

[Mesh<<<{"href": "../../../../syntax/Mesh/index.html"}>>>]
  type = GeneratedMesh
  dim = 1
  nx = 10
  xmin = -1
  xmax = 0
[]

[GlobalParams<<<{"href": "../../../../syntax/GlobalParams/index.html"}>>>]
  PorousFlowDictator = dictator
[]

[Variables<<<{"href": "../../../../syntax/Variables/index.html"}>>>]
  [ppwater]
    initial_condition<<<{"description": "Specifies a constant initial condition for this variable"}>>> = -1.0
  []
  [ppgas]
    initial_condition<<<{"description": "Specifies a constant initial condition for this variable"}>>> = 0
  []
[]

[AuxVariables<<<{"href": "../../../../syntax/AuxVariables/index.html"}>>>]
  [massfrac_ph0_sp0]
    initial_condition<<<{"description": "Specifies a constant initial condition for this variable"}>>> = 1
  []
  [massfrac_ph1_sp0]
    initial_condition<<<{"description": "Specifies a constant initial condition for this variable"}>>> = 0
  []
[]

[Kernels<<<{"href": "../../../../syntax/Kernels/index.html"}>>>]
  [flux0]
    type = PorousFlowAdvectiveFlux<<<{"description": "Fully-upwinded advective flux of the component given by fluid_component", "href": "../../../../source/kernels/PorousFlowAdvectiveFlux.html"}>>>
    fluid_component<<<{"description": "The index corresponding to the fluid component for this kernel"}>>> = 0
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = ppwater
    gravity<<<{"description": "Gravitational acceleration vector downwards (m/s^2)"}>>> = '-1 0 0'
  []
  [flux1]
    type = PorousFlowAdvectiveFlux<<<{"description": "Fully-upwinded advective flux of the component given by fluid_component", "href": "../../../../source/kernels/PorousFlowAdvectiveFlux.html"}>>>
    fluid_component<<<{"description": "The index corresponding to the fluid component for this kernel"}>>> = 1
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = ppgas
    gravity<<<{"description": "Gravitational acceleration vector downwards (m/s^2)"}>>> = '-1 0 0'
  []
[]

[BCs<<<{"href": "../../../../syntax/BCs/index.html"}>>>]
  [ppwater]
    type = DirichletBC<<<{"description": "Imposes the essential boundary condition $u=g$, where $g$ is a constant, controllable value.", "href": "../../../../source/bcs/DirichletBC.html"}>>>
    boundary<<<{"description": "The list of boundary IDs from the mesh where this object applies"}>>> = right
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = ppwater
    value<<<{"description": "Value of the BC"}>>> = -1
  []
  [ppgas]
    type = DirichletBC<<<{"description": "Imposes the essential boundary condition $u=g$, where $g$ is a constant, controllable value.", "href": "../../../../source/bcs/DirichletBC.html"}>>>
    boundary<<<{"description": "The list of boundary IDs from the mesh where this object applies"}>>> = right
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = ppgas
    value<<<{"description": "Value of the BC"}>>> = 0
  []
[]

[Functions<<<{"href": "../../../../syntax/Functions/index.html"}>>>]
  [ana_ppwater]
    type = ParsedFunction<<<{"description": "Function created by parsing a string", "href": "../../../../source/functions/MooseParsedFunction.html"}>>>
    symbol_names<<<{"description": "Symbols (excluding t,x,y,z) that are bound to the values provided by the corresponding items in the vals vector."}>>> = 'g B p0 rho0'
    symbol_values<<<{"description": "Constant numeric values, postprocessor names, function names, and scalar variables corresponding to the symbols in symbol_names."}>>> = '1 2 pp_water_top 1'
    expression<<<{"description": "The user defined function."}>>> = '-B*log(exp(-p0/B)+g*rho0*x/B)' # expected pp at base
  []
  [ana_ppgas]
    type = ParsedFunction<<<{"description": "Function created by parsing a string", "href": "../../../../source/functions/MooseParsedFunction.html"}>>>
    symbol_names<<<{"description": "Symbols (excluding t,x,y,z) that are bound to the values provided by the corresponding items in the vals vector."}>>> = 'g B p0 rho0'
    symbol_values<<<{"description": "Constant numeric values, postprocessor names, function names, and scalar variables corresponding to the symbols in symbol_names."}>>> = '1 1 pp_gas_top 0.1'
    expression<<<{"description": "The user defined function."}>>> = '-B*log(exp(-p0/B)+g*rho0*x/B)' # expected pp at base
  []
[]

[UserObjects<<<{"href": "../../../../syntax/UserObjects/index.html"}>>>]
  [dictator]
    type = PorousFlowDictator<<<{"description": "Holds information on the PorousFlow variable names", "href": "../../../../source/userobjects/PorousFlowDictator.html"}>>>
    porous_flow_vars<<<{"description": "List of primary variables that are used in the PorousFlow simulation.  Jacobian entries involving derivatives wrt these variables will be computed.  In single-phase models you will just have one (eg 'pressure'), in two-phase models you will have two (eg 'p_water p_gas', or 'p_water s_water'), etc."}>>> = 'ppwater ppgas'
    number_fluid_phases<<<{"description": "The number of fluid phases in the simulation"}>>> = 2
    number_fluid_components<<<{"description": "The number of fluid components in the simulation"}>>> = 2
  []
  [pc]
    type = PorousFlowCapillaryPressureVG<<<{"description": "van Genuchten capillary pressure", "href": "../../../../source/userobjects/PorousFlowCapillaryPressureVG.html"}>>>
    m<<<{"description": "van Genuchten exponent m. Must be between 0 and 1, and optimally should be set to >0.5"}>>> = 0.5
    alpha<<<{"description": "van Genuchten parameter alpha. Must be positive"}>>> = 1
  []
[]

[FluidProperties<<<{"href": "../../../../syntax/FluidProperties/index.html"}>>>]
  [simple_fluid0]
    type = SimpleFluidProperties<<<{"description": "Fluid properties for a simple fluid with a constant bulk density", "href": "../../../../source/fluidproperties/SimpleFluidProperties.html"}>>>
    bulk_modulus<<<{"description": "Constant bulk modulus (Pa)"}>>> = 2
    density0<<<{"description": "Density at zero pressure and zero temperature"}>>> = 1
    viscosity<<<{"description": "Constant dynamic viscosity (Pa.s)"}>>> = 1
    thermal_expansion<<<{"description": "Constant coefficient of thermal expansion (1/K)"}>>> = 0
  []
  [simple_fluid1]
    type = SimpleFluidProperties<<<{"description": "Fluid properties for a simple fluid with a constant bulk density", "href": "../../../../source/fluidproperties/SimpleFluidProperties.html"}>>>
    bulk_modulus<<<{"description": "Constant bulk modulus (Pa)"}>>> = 1
    density0<<<{"description": "Density at zero pressure and zero temperature"}>>> = 0.1
    viscosity<<<{"description": "Constant dynamic viscosity (Pa.s)"}>>> = 0.5
    thermal_expansion<<<{"description": "Constant coefficient of thermal expansion (1/K)"}>>> = 0
  []
[]

[Materials<<<{"href": "../../../../syntax/Materials/index.html"}>>>]
  [temperature]
    type = PorousFlowTemperature<<<{"description": "Material to provide temperature at the quadpoints or nodes and derivatives of it with respect to the PorousFlow variables", "href": "../../../../source/materials/PorousFlowTemperature.html"}>>>
  []
  [ppss]
    type = PorousFlow2PhasePP<<<{"description": "This Material calculates the 2 porepressures and the 2 saturations in a 2-phase situation, and derivatives of these with respect to the PorousFlowVariables", "href": "../../../../source/materials/PorousFlow2PhasePP.html"}>>>
    phase0_porepressure<<<{"description": "Variable that is the porepressure of phase 0 (eg, the water phase).  It will be <= phase1_porepressure."}>>> = ppwater
    phase1_porepressure<<<{"description": "Variable that is the porepressure of phase 1 (eg, the gas phase)"}>>> = ppgas
    capillary_pressure<<<{"description": "Name of the UserObject defining the capillary pressure"}>>> = pc
  []
  [massfrac]
    type = PorousFlowMassFraction<<<{"description": "This Material forms a std::vector<std::vector ...> of mass-fractions out of the individual mass fractions", "href": "../../../../source/materials/PorousFlowMassFraction.html"}>>>
    mass_fraction_vars<<<{"description": "List of variables that represent the mass fractions.  Format is 'f_ph0^c0 f_ph0^c1 f_ph0^c2 ... f_ph0^c(N-2) f_ph1^c0 f_ph1^c1 fph1^c2 ... fph1^c(N-2) ... fphP^c0 f_phP^c1 fphP^c2 ... fphP^c(N-2)' where N=num_components and P=num_phases, and it is assumed that f_ph^c(N-1)=1-sum(f_ph^c,{c,0,N-2}) so that f_ph^c(N-1) need not be given.  If no variables are provided then num_phases=1=num_components."}>>> = 'massfrac_ph0_sp0 massfrac_ph1_sp0'
  []
  [simple_fluid0]
    type = PorousFlowSingleComponentFluid<<<{"description": "This Material calculates fluid properties at the quadpoints or nodes for a single component fluid", "href": "../../../../source/materials/PorousFlowSingleComponentFluid.html"}>>>
    fp<<<{"description": "The name of the user object for fluid properties"}>>> = simple_fluid0
    phase<<<{"description": "The phase number"}>>> = 0
  []
  [simple_fluid1]
    type = PorousFlowSingleComponentFluid<<<{"description": "This Material calculates fluid properties at the quadpoints or nodes for a single component fluid", "href": "../../../../source/materials/PorousFlowSingleComponentFluid.html"}>>>
    fp<<<{"description": "The name of the user object for fluid properties"}>>> = simple_fluid1
    phase<<<{"description": "The phase number"}>>> = 1
  []
  [permeability]
    type = PorousFlowPermeabilityConst<<<{"description": "This Material calculates the permeability tensor assuming it is constant", "href": "../../../../source/materials/PorousFlowPermeabilityConst.html"}>>>
    permeability<<<{"description": "The permeability tensor (usually in m^2), which is assumed constant for this material"}>>> = '1 0 0  0 2 0  0 0 3'
  []
  [relperm_water]
    type = PorousFlowRelativePermeabilityCorey<<<{"description": "This Material calculates relative permeability of the fluid phase, using the simple Corey model ((S-S_res)/(1-sum(S_res)))^n", "href": "../../../../source/materials/PorousFlowRelativePermeabilityCorey.html"}>>>
    n<<<{"description": "The Corey exponent of the phase."}>>> = 1
    phase<<<{"description": "The phase number"}>>> = 0
  []
  [relperm_gas]
    type = PorousFlowRelativePermeabilityCorey<<<{"description": "This Material calculates relative permeability of the fluid phase, using the simple Corey model ((S-S_res)/(1-sum(S_res)))^n", "href": "../../../../source/materials/PorousFlowRelativePermeabilityCorey.html"}>>>
    n<<<{"description": "The Corey exponent of the phase."}>>> = 1
    phase<<<{"description": "The phase number"}>>> = 1
  []
[]

[Postprocessors<<<{"href": "../../../../syntax/Postprocessors/index.html"}>>>]
  [pp_water_top]
    type = PointValue<<<{"description": "Compute the value of a variable at a specified location", "href": "../../../../source/postprocessors/PointValue.html"}>>>
    variable<<<{"description": "The name of the variable that this postprocessor operates on."}>>> = ppwater
    point<<<{"description": "The physical point where the solution will be evaluated."}>>> = '0 0 0'
  []
  [pp_water_base]
    type = PointValue<<<{"description": "Compute the value of a variable at a specified location", "href": "../../../../source/postprocessors/PointValue.html"}>>>
    variable<<<{"description": "The name of the variable that this postprocessor operates on."}>>> = ppwater
    point<<<{"description": "The physical point where the solution will be evaluated."}>>> = '-1 0 0'
  []
  [pp_water_analytical]
    type = FunctionValuePostprocessor<<<{"description": "Computes the value of a supplied function at a single point (scalable)", "href": "../../../../source/postprocessors/FunctionValuePostprocessor.html"}>>>
    function<<<{"description": "The function which supplies the postprocessor value."}>>> = ana_ppwater
    point<<<{"description": "A set of three PostprocessorNames or constant values (or any mixture thereof) that will be passed to the function in the space argument"}>>> = '-1 0 0'
  []
  [pp_gas_top]
    type = PointValue<<<{"description": "Compute the value of a variable at a specified location", "href": "../../../../source/postprocessors/PointValue.html"}>>>
    variable<<<{"description": "The name of the variable that this postprocessor operates on."}>>> = ppgas
    point<<<{"description": "The physical point where the solution will be evaluated."}>>> = '0 0 0'
  []
  [pp_gas_base]
    type = PointValue<<<{"description": "Compute the value of a variable at a specified location", "href": "../../../../source/postprocessors/PointValue.html"}>>>
    variable<<<{"description": "The name of the variable that this postprocessor operates on."}>>> = ppgas
    point<<<{"description": "The physical point where the solution will be evaluated."}>>> = '-1 0 0'
  []
  [pp_gas_analytical]
    type = FunctionValuePostprocessor<<<{"description": "Computes the value of a supplied function at a single point (scalable)", "href": "../../../../source/postprocessors/FunctionValuePostprocessor.html"}>>>
    function<<<{"description": "The function which supplies the postprocessor value."}>>> = ana_ppgas
    point<<<{"description": "A set of three PostprocessorNames or constant values (or any mixture thereof) that will be passed to the function in the space argument"}>>> = '-1 0 0'
  []
[]

[Preconditioning<<<{"href": "../../../../syntax/Preconditioning/index.html"}>>>]
  [andy]
    type = SMP<<<{"description": "Single matrix preconditioner (SMP) builds a preconditioner using user defined off-diagonal parts of the Jacobian.", "href": "../../../../source/preconditioners/SingleMatrixPreconditioner.html"}>>>
    full<<<{"description": "Set to true if you want the full set of couplings between variables simply for convenience so you don't have to set every off_diag_row and off_diag_column combination."}>>> = true
  []
[]

[Executioner<<<{"href": "../../../../syntax/Executioner/index.html"}>>>]
  type = Steady
  solve_type = Newton
[]

[Outputs<<<{"href": "../../../../syntax/Outputs/index.html"}>>>]
  file_base<<<{"description": "Common file base name to be utilized with all output objects"}>>> = grav02b
  [csv]
    type = CSV<<<{"description": "Output for postprocessors, vector postprocessors, and scalar variables using comma seperated values (CSV).", "href": "../../../../source/outputs/CSV.html"}>>>
  []
  exodus<<<{"description": "Output the results using the default settings for Exodus output."}>>> = false
[]

A variety of transient simulations are performed. In the transient simulations, conservation of mass can be checked, and the tests demonstrate MOOSE conserves mass. Depending on the initial and boundary conditions, the "heavy" phase (with greatest mass) can completely displace the "light" phase, which is forced to move to the top of the simulation. Eq. (1) only governs the light phase in the unsaturated zone, since in the saturated zone (where there is zero light phase) the pressure must follow the heavy-phase version of Eq. (1). An example is shown in Figure 1.

Using the PP formulation with unsaturated fluids:

# Checking that gravity head is established in the transient situation when 0<saturation<1 (note the strictly less-than).
# 2phase (PP), 2components, vanGenuchten, constant fluid bulk-moduli for each phase, constant viscosity, constant permeability, Corey relative perm
# For better agreement with the analytical solution (ana_pp), just increase nx

[Mesh<<<{"href": "../../../../syntax/Mesh/index.html"}>>>]
  type = GeneratedMesh
  dim = 1
  nx = 10
  xmin = -1
  xmax = 0
[]

[GlobalParams<<<{"href": "../../../../syntax/GlobalParams/index.html"}>>>]
  PorousFlowDictator = dictator
[]

[Variables<<<{"href": "../../../../syntax/Variables/index.html"}>>>]
  [ppwater]
    initial_condition<<<{"description": "Specifies a constant initial condition for this variable"}>>> = -1.0
  []
  [ppgas]
    initial_condition<<<{"description": "Specifies a constant initial condition for this variable"}>>> = 0
  []
[]

[AuxVariables<<<{"href": "../../../../syntax/AuxVariables/index.html"}>>>]
  [massfrac_ph0_sp0]
    initial_condition<<<{"description": "Specifies a constant initial condition for this variable"}>>> = 1
  []
  [massfrac_ph1_sp0]
    initial_condition<<<{"description": "Specifies a constant initial condition for this variable"}>>> = 0
  []
[]

[Kernels<<<{"href": "../../../../syntax/Kernels/index.html"}>>>]
  [mass0]
    type = PorousFlowMassTimeDerivative<<<{"description": "Derivative of fluid-component mass with respect to time.  Mass lumping to the nodes is used.", "href": "../../../../source/kernels/PorousFlowMassTimeDerivative.html"}>>>
    fluid_component<<<{"description": "The index corresponding to the component for this kernel"}>>> = 0
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = ppwater
  []
  [flux0]
    type = PorousFlowAdvectiveFlux<<<{"description": "Fully-upwinded advective flux of the component given by fluid_component", "href": "../../../../source/kernels/PorousFlowAdvectiveFlux.html"}>>>
    fluid_component<<<{"description": "The index corresponding to the fluid component for this kernel"}>>> = 0
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = ppwater
    gravity<<<{"description": "Gravitational acceleration vector downwards (m/s^2)"}>>> = '-1 0 0'
  []
  [mass1]
    type = PorousFlowMassTimeDerivative<<<{"description": "Derivative of fluid-component mass with respect to time.  Mass lumping to the nodes is used.", "href": "../../../../source/kernels/PorousFlowMassTimeDerivative.html"}>>>
    fluid_component<<<{"description": "The index corresponding to the component for this kernel"}>>> = 1
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = ppgas
  []
  [flux1]
    type = PorousFlowAdvectiveFlux<<<{"description": "Fully-upwinded advective flux of the component given by fluid_component", "href": "../../../../source/kernels/PorousFlowAdvectiveFlux.html"}>>>
    fluid_component<<<{"description": "The index corresponding to the fluid component for this kernel"}>>> = 1
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = ppgas
    gravity<<<{"description": "Gravitational acceleration vector downwards (m/s^2)"}>>> = '-1 0 0'
  []
[]

[Functions<<<{"href": "../../../../syntax/Functions/index.html"}>>>]
  [ana_ppwater]
    type = ParsedFunction<<<{"description": "Function created by parsing a string", "href": "../../../../source/functions/MooseParsedFunction.html"}>>>
    symbol_names<<<{"description": "Symbols (excluding t,x,y,z) that are bound to the values provided by the corresponding items in the vals vector."}>>> = 'g B p0 rho0'
    symbol_values<<<{"description": "Constant numeric values, postprocessor names, function names, and scalar variables corresponding to the symbols in symbol_names."}>>> = '1 2 pp_water_top 1'
    expression<<<{"description": "The user defined function."}>>> = '-B*log(exp(-p0/B)+g*rho0*x/B)' # expected pp at base
  []
  [ana_ppgas]
    type = ParsedFunction<<<{"description": "Function created by parsing a string", "href": "../../../../source/functions/MooseParsedFunction.html"}>>>
    symbol_names<<<{"description": "Symbols (excluding t,x,y,z) that are bound to the values provided by the corresponding items in the vals vector."}>>> = 'g B p0 rho0'
    symbol_values<<<{"description": "Constant numeric values, postprocessor names, function names, and scalar variables corresponding to the symbols in symbol_names."}>>> = '1 1 pp_gas_top 0.1'
    expression<<<{"description": "The user defined function."}>>> = '-B*log(exp(-p0/B)+g*rho0*x/B)' # expected pp at base
  []
[]

[UserObjects<<<{"href": "../../../../syntax/UserObjects/index.html"}>>>]
  [dictator]
    type = PorousFlowDictator<<<{"description": "Holds information on the PorousFlow variable names", "href": "../../../../source/userobjects/PorousFlowDictator.html"}>>>
    porous_flow_vars<<<{"description": "List of primary variables that are used in the PorousFlow simulation.  Jacobian entries involving derivatives wrt these variables will be computed.  In single-phase models you will just have one (eg 'pressure'), in two-phase models you will have two (eg 'p_water p_gas', or 'p_water s_water'), etc."}>>> = 'ppwater ppgas'
    number_fluid_phases<<<{"description": "The number of fluid phases in the simulation"}>>> = 2
    number_fluid_components<<<{"description": "The number of fluid components in the simulation"}>>> = 2
  []
  [pc]
    type = PorousFlowCapillaryPressureVG<<<{"description": "van Genuchten capillary pressure", "href": "../../../../source/userobjects/PorousFlowCapillaryPressureVG.html"}>>>
    m<<<{"description": "van Genuchten exponent m. Must be between 0 and 1, and optimally should be set to >0.5"}>>> = 0.5
    alpha<<<{"description": "van Genuchten parameter alpha. Must be positive"}>>> = 1
  []
[]

[FluidProperties<<<{"href": "../../../../syntax/FluidProperties/index.html"}>>>]
  [simple_fluid0]
    type = SimpleFluidProperties<<<{"description": "Fluid properties for a simple fluid with a constant bulk density", "href": "../../../../source/fluidproperties/SimpleFluidProperties.html"}>>>
    bulk_modulus<<<{"description": "Constant bulk modulus (Pa)"}>>> = 2
    density0<<<{"description": "Density at zero pressure and zero temperature"}>>> = 1
    viscosity<<<{"description": "Constant dynamic viscosity (Pa.s)"}>>> = 1
    thermal_expansion<<<{"description": "Constant coefficient of thermal expansion (1/K)"}>>> = 0
  []
  [simple_fluid1]
    type = SimpleFluidProperties<<<{"description": "Fluid properties for a simple fluid with a constant bulk density", "href": "../../../../source/fluidproperties/SimpleFluidProperties.html"}>>>
    bulk_modulus<<<{"description": "Constant bulk modulus (Pa)"}>>> = 1
    density0<<<{"description": "Density at zero pressure and zero temperature"}>>> = 0.1
    viscosity<<<{"description": "Constant dynamic viscosity (Pa.s)"}>>> = 0.5
    thermal_expansion<<<{"description": "Constant coefficient of thermal expansion (1/K)"}>>> = 0
  []
[]

[Materials<<<{"href": "../../../../syntax/Materials/index.html"}>>>]
  [temperature]
    type = PorousFlowTemperature<<<{"description": "Material to provide temperature at the quadpoints or nodes and derivatives of it with respect to the PorousFlow variables", "href": "../../../../source/materials/PorousFlowTemperature.html"}>>>
  []
  [ppss]
    type = PorousFlow2PhasePP<<<{"description": "This Material calculates the 2 porepressures and the 2 saturations in a 2-phase situation, and derivatives of these with respect to the PorousFlowVariables", "href": "../../../../source/materials/PorousFlow2PhasePP.html"}>>>
    phase0_porepressure<<<{"description": "Variable that is the porepressure of phase 0 (eg, the water phase).  It will be <= phase1_porepressure."}>>> = ppwater
    phase1_porepressure<<<{"description": "Variable that is the porepressure of phase 1 (eg, the gas phase)"}>>> = ppgas
    capillary_pressure<<<{"description": "Name of the UserObject defining the capillary pressure"}>>> = pc
  []
  [massfrac]
    type = PorousFlowMassFraction<<<{"description": "This Material forms a std::vector<std::vector ...> of mass-fractions out of the individual mass fractions", "href": "../../../../source/materials/PorousFlowMassFraction.html"}>>>
    mass_fraction_vars<<<{"description": "List of variables that represent the mass fractions.  Format is 'f_ph0^c0 f_ph0^c1 f_ph0^c2 ... f_ph0^c(N-2) f_ph1^c0 f_ph1^c1 fph1^c2 ... fph1^c(N-2) ... fphP^c0 f_phP^c1 fphP^c2 ... fphP^c(N-2)' where N=num_components and P=num_phases, and it is assumed that f_ph^c(N-1)=1-sum(f_ph^c,{c,0,N-2}) so that f_ph^c(N-1) need not be given.  If no variables are provided then num_phases=1=num_components."}>>> = 'massfrac_ph0_sp0 massfrac_ph1_sp0'
  []
  [simple_fluid0]
    type = PorousFlowSingleComponentFluid<<<{"description": "This Material calculates fluid properties at the quadpoints or nodes for a single component fluid", "href": "../../../../source/materials/PorousFlowSingleComponentFluid.html"}>>>
    fp<<<{"description": "The name of the user object for fluid properties"}>>> = simple_fluid0
    phase<<<{"description": "The phase number"}>>> = 0
  []
  [simple_fluid1]
    type = PorousFlowSingleComponentFluid<<<{"description": "This Material calculates fluid properties at the quadpoints or nodes for a single component fluid", "href": "../../../../source/materials/PorousFlowSingleComponentFluid.html"}>>>
    fp<<<{"description": "The name of the user object for fluid properties"}>>> = simple_fluid1
    phase<<<{"description": "The phase number"}>>> = 1
  []
  [porosity]
    type = PorousFlowPorosityConst<<<{"description": "This Material calculates the porosity assuming it is constant", "href": "../../../../source/materials/PorousFlowPorosityConst.html"}>>>
    porosity<<<{"description": "The porosity (assumed indepenent of porepressure, temperature, strain, etc, for this material).  This should be a real number, or a constant monomial variable (not a linear lagrange or other kind of variable)."}>>> = 0.1
  []
  [permeability]
    type = PorousFlowPermeabilityConst<<<{"description": "This Material calculates the permeability tensor assuming it is constant", "href": "../../../../source/materials/PorousFlowPermeabilityConst.html"}>>>
    permeability<<<{"description": "The permeability tensor (usually in m^2), which is assumed constant for this material"}>>> = '1 0 0  0 2 0  0 0 3'
  []
  [relperm_water]
    type = PorousFlowRelativePermeabilityCorey<<<{"description": "This Material calculates relative permeability of the fluid phase, using the simple Corey model ((S-S_res)/(1-sum(S_res)))^n", "href": "../../../../source/materials/PorousFlowRelativePermeabilityCorey.html"}>>>
    n<<<{"description": "The Corey exponent of the phase."}>>> = 1
    phase<<<{"description": "The phase number"}>>> = 0
  []
  [relperm_gas]
    type = PorousFlowRelativePermeabilityCorey<<<{"description": "This Material calculates relative permeability of the fluid phase, using the simple Corey model ((S-S_res)/(1-sum(S_res)))^n", "href": "../../../../source/materials/PorousFlowRelativePermeabilityCorey.html"}>>>
    n<<<{"description": "The Corey exponent of the phase."}>>> = 1
    phase<<<{"description": "The phase number"}>>> = 1
  []
[]

[Postprocessors<<<{"href": "../../../../syntax/Postprocessors/index.html"}>>>]
  [pp_water_top]
    type = PointValue<<<{"description": "Compute the value of a variable at a specified location", "href": "../../../../source/postprocessors/PointValue.html"}>>>
    variable<<<{"description": "The name of the variable that this postprocessor operates on."}>>> = ppwater
    point<<<{"description": "The physical point where the solution will be evaluated."}>>> = '0 0 0'
  []
  [pp_water_base]
    type = PointValue<<<{"description": "Compute the value of a variable at a specified location", "href": "../../../../source/postprocessors/PointValue.html"}>>>
    variable<<<{"description": "The name of the variable that this postprocessor operates on."}>>> = ppwater
    point<<<{"description": "The physical point where the solution will be evaluated."}>>> = '-1 0 0'
  []
  [pp_water_analytical]
    type = FunctionValuePostprocessor<<<{"description": "Computes the value of a supplied function at a single point (scalable)", "href": "../../../../source/postprocessors/FunctionValuePostprocessor.html"}>>>
    function<<<{"description": "The function which supplies the postprocessor value."}>>> = ana_ppwater
    point<<<{"description": "A set of three PostprocessorNames or constant values (or any mixture thereof) that will be passed to the function in the space argument"}>>> = '-1 0 0'
  []
  [pp_gas_top]
    type = PointValue<<<{"description": "Compute the value of a variable at a specified location", "href": "../../../../source/postprocessors/PointValue.html"}>>>
    variable<<<{"description": "The name of the variable that this postprocessor operates on."}>>> = ppgas
    point<<<{"description": "The physical point where the solution will be evaluated."}>>> = '0 0 0'
  []
  [pp_gas_base]
    type = PointValue<<<{"description": "Compute the value of a variable at a specified location", "href": "../../../../source/postprocessors/PointValue.html"}>>>
    variable<<<{"description": "The name of the variable that this postprocessor operates on."}>>> = ppgas
    point<<<{"description": "The physical point where the solution will be evaluated."}>>> = '-1 0 0'
  []
  [pp_gas_analytical]
    type = FunctionValuePostprocessor<<<{"description": "Computes the value of a supplied function at a single point (scalable)", "href": "../../../../source/postprocessors/FunctionValuePostprocessor.html"}>>>
    function<<<{"description": "The function which supplies the postprocessor value."}>>> = ana_ppgas
    point<<<{"description": "A set of three PostprocessorNames or constant values (or any mixture thereof) that will be passed to the function in the space argument"}>>> = '-1 0 0'
  []
  [mass_ph0]
    type = PorousFlowFluidMass<<<{"description": "Calculates the mass of a fluid component in a region", "href": "../../../../source/postprocessors/PorousFlowFluidMass.html"}>>>
    fluid_component<<<{"description": "The index corresponding to the fluid component that this Postprocessor acts on"}>>> = 0
    execute_on<<<{"description": "The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html."}>>> = 'initial timestep_end'
  []
  [mass_ph1]
    type = PorousFlowFluidMass<<<{"description": "Calculates the mass of a fluid component in a region", "href": "../../../../source/postprocessors/PorousFlowFluidMass.html"}>>>
    fluid_component<<<{"description": "The index corresponding to the fluid component that this Postprocessor acts on"}>>> = 1
    execute_on<<<{"description": "The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html."}>>> = 'initial timestep_end'
  []
[]

[Preconditioning<<<{"href": "../../../../syntax/Preconditioning/index.html"}>>>]
  [andy]
    type = SMP<<<{"description": "Single matrix preconditioner (SMP) builds a preconditioner using user defined off-diagonal parts of the Jacobian.", "href": "../../../../source/preconditioners/SingleMatrixPreconditioner.html"}>>>
    full<<<{"description": "Set to true if you want the full set of couplings between variables simply for convenience so you don't have to set every off_diag_row and off_diag_column combination."}>>> = true
  []
[]

[Executioner<<<{"href": "../../../../syntax/Executioner/index.html"}>>>]
  type = Transient
  solve_type = Newton
  dt = 0.1
  end_time = 1.0
  nl_rel_tol = 1E-10
  nl_abs_tol = 1E-12
[]

[Outputs<<<{"href": "../../../../syntax/Outputs/index.html"}>>>]
  [csv]
    type = CSV<<<{"description": "Output for postprocessors, vector postprocessors, and scalar variables using comma seperated values (CSV).", "href": "../../../../source/outputs/CSV.html"}>>>
    file_base<<<{"description": "The desired solution output name without an extension. If not provided, MOOSE sets it with Outputs/file_base when available. Otherwise, MOOSE uses input file name and this object name for a master input or uses master file_base, the subapp name and this object name for a subapp input to set it."}>>> = grav02a
    execute_on<<<{"description": "The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html."}>>> = 'initial final'
  []
[]

Using the PP formulation with saturated and unsaturated fluids::

# Checking that gravity head is established in the transient situation when 0<=saturation<=1 (note the less-than-or-equal-to).
# 2phase (PP), 2components, vanGenuchten, constant fluid bulk-moduli for each phase, constant viscosity, constant permeability, Corey relative perm
# For better agreement with the analytical solution (ana_pp), just increase nx

[Mesh<<<{"href": "../../../../syntax/Mesh/index.html"}>>>]
  type = GeneratedMesh
  dim = 1
  nx = 10
  xmin = -1
  xmax = 0
[]

[GlobalParams<<<{"href": "../../../../syntax/GlobalParams/index.html"}>>>]
  PorousFlowDictator = dictator
[]

[Functions<<<{"href": "../../../../syntax/Functions/index.html"}>>>]
  [dts]
    type = PiecewiseLinear<<<{"description": "Linearly interpolates between pairs of x-y data", "href": "../../../../source/functions/PiecewiseLinear.html"}>>>
    y<<<{"description": "The ordinate values"}>>> = '1E-3 1E-2 1E-1'
    x<<<{"description": "The abscissa values"}>>> = '1E-3 1E-2 1E-1'
  []
[]

[Variables<<<{"href": "../../../../syntax/Variables/index.html"}>>>]
  [ppwater]
    initial_condition<<<{"description": "Specifies a constant initial condition for this variable"}>>> = -0.1
  []
  [ppgas]
    initial_condition<<<{"description": "Specifies a constant initial condition for this variable"}>>> = 0
  []
[]

[AuxVariables<<<{"href": "../../../../syntax/AuxVariables/index.html"}>>>]
  [massfrac_ph0_sp0]
    initial_condition<<<{"description": "Specifies a constant initial condition for this variable"}>>> = 1
  []
  [massfrac_ph1_sp0]
    initial_condition<<<{"description": "Specifies a constant initial condition for this variable"}>>> = 0
  []
[]

[Kernels<<<{"href": "../../../../syntax/Kernels/index.html"}>>>]
  [mass0]
    type = PorousFlowMassTimeDerivative<<<{"description": "Derivative of fluid-component mass with respect to time.  Mass lumping to the nodes is used.", "href": "../../../../source/kernels/PorousFlowMassTimeDerivative.html"}>>>
    fluid_component<<<{"description": "The index corresponding to the component for this kernel"}>>> = 0
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = ppwater
  []
  [flux0]
    type = PorousFlowAdvectiveFlux<<<{"description": "Fully-upwinded advective flux of the component given by fluid_component", "href": "../../../../source/kernels/PorousFlowAdvectiveFlux.html"}>>>
    fluid_component<<<{"description": "The index corresponding to the fluid component for this kernel"}>>> = 0
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = ppwater
    gravity<<<{"description": "Gravitational acceleration vector downwards (m/s^2)"}>>> = '-1 0 0'
  []
  [mass1]
    type = PorousFlowMassTimeDerivative<<<{"description": "Derivative of fluid-component mass with respect to time.  Mass lumping to the nodes is used.", "href": "../../../../source/kernels/PorousFlowMassTimeDerivative.html"}>>>
    fluid_component<<<{"description": "The index corresponding to the component for this kernel"}>>> = 1
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = ppgas
  []
  [flux1]
    type = PorousFlowAdvectiveFlux<<<{"description": "Fully-upwinded advective flux of the component given by fluid_component", "href": "../../../../source/kernels/PorousFlowAdvectiveFlux.html"}>>>
    fluid_component<<<{"description": "The index corresponding to the fluid component for this kernel"}>>> = 1
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = ppgas
    gravity<<<{"description": "Gravitational acceleration vector downwards (m/s^2)"}>>> = '-1 0 0'
  []
[]

[Functions]
  [ana_ppwater]
    type = ParsedFunction<<<{"description": "Function created by parsing a string", "href": "../../../../source/functions/MooseParsedFunction.html"}>>>
    symbol_names<<<{"description": "Symbols (excluding t,x,y,z) that are bound to the values provided by the corresponding items in the vals vector."}>>> = 'g B p0 rho0'
    symbol_values<<<{"description": "Constant numeric values, postprocessor names, function names, and scalar variables corresponding to the symbols in symbol_names."}>>> = '1 2 pp_water_top 1'
    expression<<<{"description": "The user defined function."}>>> = '-B*log(exp(-p0/B)+g*rho0*x/B)' # expected pp at base
  []
[]

[UserObjects<<<{"href": "../../../../syntax/UserObjects/index.html"}>>>]
  [dictator]
    type = PorousFlowDictator<<<{"description": "Holds information on the PorousFlow variable names", "href": "../../../../source/userobjects/PorousFlowDictator.html"}>>>
    porous_flow_vars<<<{"description": "List of primary variables that are used in the PorousFlow simulation.  Jacobian entries involving derivatives wrt these variables will be computed.  In single-phase models you will just have one (eg 'pressure'), in two-phase models you will have two (eg 'p_water p_gas', or 'p_water s_water'), etc."}>>> = 'ppwater ppgas'
    number_fluid_phases<<<{"description": "The number of fluid phases in the simulation"}>>> = 2
    number_fluid_components<<<{"description": "The number of fluid components in the simulation"}>>> = 2
  []
  [pc]
    type = PorousFlowCapillaryPressureVG<<<{"description": "van Genuchten capillary pressure", "href": "../../../../source/userobjects/PorousFlowCapillaryPressureVG.html"}>>>
    m<<<{"description": "van Genuchten exponent m. Must be between 0 and 1, and optimally should be set to >0.5"}>>> = 0.5
    alpha<<<{"description": "van Genuchten parameter alpha. Must be positive"}>>> = 1
  []
[]

[FluidProperties<<<{"href": "../../../../syntax/FluidProperties/index.html"}>>>]
  [simple_fluid0]
    type = SimpleFluidProperties<<<{"description": "Fluid properties for a simple fluid with a constant bulk density", "href": "../../../../source/fluidproperties/SimpleFluidProperties.html"}>>>
    bulk_modulus<<<{"description": "Constant bulk modulus (Pa)"}>>> = 2
    density0<<<{"description": "Density at zero pressure and zero temperature"}>>> = 1
    viscosity<<<{"description": "Constant dynamic viscosity (Pa.s)"}>>> = 1
    thermal_expansion<<<{"description": "Constant coefficient of thermal expansion (1/K)"}>>> = 0
  []
  [simple_fluid1]
    type = SimpleFluidProperties<<<{"description": "Fluid properties for a simple fluid with a constant bulk density", "href": "../../../../source/fluidproperties/SimpleFluidProperties.html"}>>>
    bulk_modulus<<<{"description": "Constant bulk modulus (Pa)"}>>> = 1
    density0<<<{"description": "Density at zero pressure and zero temperature"}>>> = 0.1
    viscosity<<<{"description": "Constant dynamic viscosity (Pa.s)"}>>> = 0.5
    thermal_expansion<<<{"description": "Constant coefficient of thermal expansion (1/K)"}>>> = 0
  []
[]

[Materials<<<{"href": "../../../../syntax/Materials/index.html"}>>>]
  [temperature]
    type = PorousFlowTemperature<<<{"description": "Material to provide temperature at the quadpoints or nodes and derivatives of it with respect to the PorousFlow variables", "href": "../../../../source/materials/PorousFlowTemperature.html"}>>>
  []
  [ppss]
    type = PorousFlow2PhasePP<<<{"description": "This Material calculates the 2 porepressures and the 2 saturations in a 2-phase situation, and derivatives of these with respect to the PorousFlowVariables", "href": "../../../../source/materials/PorousFlow2PhasePP.html"}>>>
    phase0_porepressure<<<{"description": "Variable that is the porepressure of phase 0 (eg, the water phase).  It will be <= phase1_porepressure."}>>> = ppwater
    phase1_porepressure<<<{"description": "Variable that is the porepressure of phase 1 (eg, the gas phase)"}>>> = ppgas
    capillary_pressure<<<{"description": "Name of the UserObject defining the capillary pressure"}>>> = pc
  []
  [massfrac]
    type = PorousFlowMassFraction<<<{"description": "This Material forms a std::vector<std::vector ...> of mass-fractions out of the individual mass fractions", "href": "../../../../source/materials/PorousFlowMassFraction.html"}>>>
    mass_fraction_vars<<<{"description": "List of variables that represent the mass fractions.  Format is 'f_ph0^c0 f_ph0^c1 f_ph0^c2 ... f_ph0^c(N-2) f_ph1^c0 f_ph1^c1 fph1^c2 ... fph1^c(N-2) ... fphP^c0 f_phP^c1 fphP^c2 ... fphP^c(N-2)' where N=num_components and P=num_phases, and it is assumed that f_ph^c(N-1)=1-sum(f_ph^c,{c,0,N-2}) so that f_ph^c(N-1) need not be given.  If no variables are provided then num_phases=1=num_components."}>>> = 'massfrac_ph0_sp0 massfrac_ph1_sp0'
  []
  [simple_fluid0]
    type = PorousFlowSingleComponentFluid<<<{"description": "This Material calculates fluid properties at the quadpoints or nodes for a single component fluid", "href": "../../../../source/materials/PorousFlowSingleComponentFluid.html"}>>>
    fp<<<{"description": "The name of the user object for fluid properties"}>>> = simple_fluid0
    phase<<<{"description": "The phase number"}>>> = 0
  []
  [simple_fluid1]
    type = PorousFlowSingleComponentFluid<<<{"description": "This Material calculates fluid properties at the quadpoints or nodes for a single component fluid", "href": "../../../../source/materials/PorousFlowSingleComponentFluid.html"}>>>
    fp<<<{"description": "The name of the user object for fluid properties"}>>> = simple_fluid1
    phase<<<{"description": "The phase number"}>>> = 1
  []
  [porosity]
    type = PorousFlowPorosityConst<<<{"description": "This Material calculates the porosity assuming it is constant", "href": "../../../../source/materials/PorousFlowPorosityConst.html"}>>>
    porosity<<<{"description": "The porosity (assumed indepenent of porepressure, temperature, strain, etc, for this material).  This should be a real number, or a constant monomial variable (not a linear lagrange or other kind of variable)."}>>> = 0.1
  []
  [permeability]
    type = PorousFlowPermeabilityConst<<<{"description": "This Material calculates the permeability tensor assuming it is constant", "href": "../../../../source/materials/PorousFlowPermeabilityConst.html"}>>>
    permeability<<<{"description": "The permeability tensor (usually in m^2), which is assumed constant for this material"}>>> = '1 0 0  0 2 0  0 0 3'
  []
  [relperm_water]
    type = PorousFlowRelativePermeabilityCorey<<<{"description": "This Material calculates relative permeability of the fluid phase, using the simple Corey model ((S-S_res)/(1-sum(S_res)))^n", "href": "../../../../source/materials/PorousFlowRelativePermeabilityCorey.html"}>>>
    n<<<{"description": "The Corey exponent of the phase."}>>> = 1
    phase<<<{"description": "The phase number"}>>> = 0
  []
  [relperm_gas]
    type = PorousFlowRelativePermeabilityCorey<<<{"description": "This Material calculates relative permeability of the fluid phase, using the simple Corey model ((S-S_res)/(1-sum(S_res)))^n", "href": "../../../../source/materials/PorousFlowRelativePermeabilityCorey.html"}>>>
    n<<<{"description": "The Corey exponent of the phase."}>>> = 1
    phase<<<{"description": "The phase number"}>>> = 1
  []
[]

[Postprocessors<<<{"href": "../../../../syntax/Postprocessors/index.html"}>>>]
  [pp_water_top]
    type = PointValue<<<{"description": "Compute the value of a variable at a specified location", "href": "../../../../source/postprocessors/PointValue.html"}>>>
    variable<<<{"description": "The name of the variable that this postprocessor operates on."}>>> = ppwater
    point<<<{"description": "The physical point where the solution will be evaluated."}>>> = '0 0 0'
  []
  [pp_water_base]
    type = PointValue<<<{"description": "Compute the value of a variable at a specified location", "href": "../../../../source/postprocessors/PointValue.html"}>>>
    variable<<<{"description": "The name of the variable that this postprocessor operates on."}>>> = ppwater
    point<<<{"description": "The physical point where the solution will be evaluated."}>>> = '-1 0 0'
  []
  [pp_water_analytical]
    type = FunctionValuePostprocessor<<<{"description": "Computes the value of a supplied function at a single point (scalable)", "href": "../../../../source/postprocessors/FunctionValuePostprocessor.html"}>>>
    function<<<{"description": "The function which supplies the postprocessor value."}>>> = ana_ppwater
    point<<<{"description": "A set of three PostprocessorNames or constant values (or any mixture thereof) that will be passed to the function in the space argument"}>>> = '-1 0 0'
  []
  [mass_ph0]
    type = PorousFlowFluidMass<<<{"description": "Calculates the mass of a fluid component in a region", "href": "../../../../source/postprocessors/PorousFlowFluidMass.html"}>>>
    fluid_component<<<{"description": "The index corresponding to the fluid component that this Postprocessor acts on"}>>> = 0
    execute_on<<<{"description": "The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html."}>>> = 'initial timestep_end'
  []
  [mass_ph1]
    type = PorousFlowFluidMass<<<{"description": "Calculates the mass of a fluid component in a region", "href": "../../../../source/postprocessors/PorousFlowFluidMass.html"}>>>
    fluid_component<<<{"description": "The index corresponding to the fluid component that this Postprocessor acts on"}>>> = 1
    execute_on<<<{"description": "The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html."}>>> = 'initial timestep_end'
  []

[]

[Preconditioning<<<{"href": "../../../../syntax/Preconditioning/index.html"}>>>]
  active<<<{"description": "If specified only the blocks named will be visited and made active"}>>> = andy
  [andy]
    type = SMP<<<{"description": "Single matrix preconditioner (SMP) builds a preconditioner using user defined off-diagonal parts of the Jacobian.", "href": "../../../../source/preconditioners/SingleMatrixPreconditioner.html"}>>>
    full<<<{"description": "Set to true if you want the full set of couplings between variables simply for convenience so you don't have to set every off_diag_row and off_diag_column combination."}>>> = true
    petsc_options_iname<<<{"description": "Names of PETSc name/value pairs"}>>> = '-ksp_type -pc_type -snes_atol -snes_rtol -snes_max_it'
    petsc_options_value<<<{"description": "Values of PETSc name/value pairs (must correspond with \"petsc_options_iname\""}>>> = 'bcgs bjacobi 1E-12 1E-10 10000'
  []
  [check]
    type = SMP<<<{"description": "Single matrix preconditioner (SMP) builds a preconditioner using user defined off-diagonal parts of the Jacobian.", "href": "../../../../source/preconditioners/SingleMatrixPreconditioner.html"}>>>
    full<<<{"description": "Set to true if you want the full set of couplings between variables simply for convenience so you don't have to set every off_diag_row and off_diag_column combination."}>>> = true
    petsc_options_iname<<<{"description": "Names of PETSc name/value pairs"}>>> = '-ksp_type -pc_type -snes_atol -snes_rtol -snes_max_it -snes_type'
    petsc_options_value<<<{"description": "Values of PETSc name/value pairs (must correspond with \"petsc_options_iname\""}>>> = 'bcgs bjacobi 1E-12 1E-10 10000 test'
  []
[]

[Executioner<<<{"href": "../../../../syntax/Executioner/index.html"}>>>]
  type = Transient
  solve_type = Newton
  [TimeStepper<<<{"href": "../../../../syntax/Executioner/TimeStepper/index.html"}>>>]
    type = FunctionDT
    function = dts
  []
  end_time = 1.0
[]

[Outputs<<<{"href": "../../../../syntax/Outputs/index.html"}>>>]
  execute_on<<<{"description": "The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html."}>>> = 'initial timestep_end'
  file_base<<<{"description": "Common file base name to be utilized with all output objects"}>>> = grav02c
  [csv]
    type = CSV<<<{"description": "Output for postprocessors, vector postprocessors, and scalar variables using comma seperated values (CSV).", "href": "../../../../source/outputs/CSV.html"}>>>
  []
  exodus<<<{"description": "Output the results using the default settings for Exodus output."}>>> = true
[]

Using the PP formulation with a boundary condition fixing porepressures:

# Checking that gravity head is established in the transient situation when 0<=saturation<=1 (note the less-than-or-equal-to).
# 2phase (PP), 2components, vanGenuchten, constant fluid bulk-moduli for each phase, constant viscosity, constant permeability, Corey relative perm.
# A boundary condition enforces porepressures at the right boundary
# For better agreement with the analytical solution (ana_pp), just increase nx

[Mesh<<<{"href": "../../../../syntax/Mesh/index.html"}>>>]
  type = GeneratedMesh
  dim = 1
  nx = 10
  xmin = -1
  xmax = 0
[]

[GlobalParams<<<{"href": "../../../../syntax/GlobalParams/index.html"}>>>]
  PorousFlowDictator = dictator
[]

[Functions<<<{"href": "../../../../syntax/Functions/index.html"}>>>]
  [dts]
    type = PiecewiseLinear<<<{"description": "Linearly interpolates between pairs of x-y data", "href": "../../../../source/functions/PiecewiseLinear.html"}>>>
    x<<<{"description": "The abscissa values"}>>> = '1E-3 1E-2 1E-1 2E-1'
    y<<<{"description": "The ordinate values"}>>> = '1E-3 1E-2 0.2E-1 1E-1'
  []
[]

[Variables<<<{"href": "../../../../syntax/Variables/index.html"}>>>]
  [ppwater]
    initial_condition<<<{"description": "Specifies a constant initial condition for this variable"}>>> = 0
  []
  [ppgas]
    initial_condition<<<{"description": "Specifies a constant initial condition for this variable"}>>> = 0.5
  []
[]

[AuxVariables<<<{"href": "../../../../syntax/AuxVariables/index.html"}>>>]
  [massfrac_ph0_sp0]
    initial_condition<<<{"description": "Specifies a constant initial condition for this variable"}>>> = 1
  []
  [massfrac_ph1_sp0]
    initial_condition<<<{"description": "Specifies a constant initial condition for this variable"}>>> = 0
  []
[]

[BCs<<<{"href": "../../../../syntax/BCs/index.html"}>>>]
  [ppwater]
    type = DirichletBC<<<{"description": "Imposes the essential boundary condition $u=g$, where $g$ is a constant, controllable value.", "href": "../../../../source/bcs/DirichletBC.html"}>>>
    boundary<<<{"description": "The list of boundary IDs from the mesh where this object applies"}>>> = right
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = ppwater
    value<<<{"description": "Value of the BC"}>>> = 0
  []
  [ppgas]
    type = DirichletBC<<<{"description": "Imposes the essential boundary condition $u=g$, where $g$ is a constant, controllable value.", "href": "../../../../source/bcs/DirichletBC.html"}>>>
    boundary<<<{"description": "The list of boundary IDs from the mesh where this object applies"}>>> = right
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = ppgas
    value<<<{"description": "Value of the BC"}>>> = 0.5
  []
[]

[Kernels<<<{"href": "../../../../syntax/Kernels/index.html"}>>>]
  [mass0]
    type = PorousFlowMassTimeDerivative<<<{"description": "Derivative of fluid-component mass with respect to time.  Mass lumping to the nodes is used.", "href": "../../../../source/kernels/PorousFlowMassTimeDerivative.html"}>>>
    fluid_component<<<{"description": "The index corresponding to the component for this kernel"}>>> = 0
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = ppwater
  []
  [flux0]
    type = PorousFlowAdvectiveFlux<<<{"description": "Fully-upwinded advective flux of the component given by fluid_component", "href": "../../../../source/kernels/PorousFlowAdvectiveFlux.html"}>>>
    fluid_component<<<{"description": "The index corresponding to the fluid component for this kernel"}>>> = 0
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = ppwater
    gravity<<<{"description": "Gravitational acceleration vector downwards (m/s^2)"}>>> = '-1 0 0'
  []
  [mass1]
    type = PorousFlowMassTimeDerivative<<<{"description": "Derivative of fluid-component mass with respect to time.  Mass lumping to the nodes is used.", "href": "../../../../source/kernels/PorousFlowMassTimeDerivative.html"}>>>
    fluid_component<<<{"description": "The index corresponding to the component for this kernel"}>>> = 1
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = ppgas
  []
  [flux1]
    type = PorousFlowAdvectiveFlux<<<{"description": "Fully-upwinded advective flux of the component given by fluid_component", "href": "../../../../source/kernels/PorousFlowAdvectiveFlux.html"}>>>
    fluid_component<<<{"description": "The index corresponding to the fluid component for this kernel"}>>> = 1
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = ppgas
    gravity<<<{"description": "Gravitational acceleration vector downwards (m/s^2)"}>>> = '-1 0 0'
  []
[]

[Functions]
  [ana_ppwater]
    type = ParsedFunction<<<{"description": "Function created by parsing a string", "href": "../../../../source/functions/MooseParsedFunction.html"}>>>
    symbol_names<<<{"description": "Symbols (excluding t,x,y,z) that are bound to the values provided by the corresponding items in the vals vector."}>>> = 'g B p0 rho0'
    symbol_values<<<{"description": "Constant numeric values, postprocessor names, function names, and scalar variables corresponding to the symbols in symbol_names."}>>> = '1 2 pp_water_top 1'
    expression<<<{"description": "The user defined function."}>>> = '-B*log(exp(-p0/B)+g*rho0*x/B)' # expected pp at base
  []
[]

[UserObjects<<<{"href": "../../../../syntax/UserObjects/index.html"}>>>]
  [dictator]
    type = PorousFlowDictator<<<{"description": "Holds information on the PorousFlow variable names", "href": "../../../../source/userobjects/PorousFlowDictator.html"}>>>
    porous_flow_vars<<<{"description": "List of primary variables that are used in the PorousFlow simulation.  Jacobian entries involving derivatives wrt these variables will be computed.  In single-phase models you will just have one (eg 'pressure'), in two-phase models you will have two (eg 'p_water p_gas', or 'p_water s_water'), etc."}>>> = 'ppwater ppgas'
    number_fluid_phases<<<{"description": "The number of fluid phases in the simulation"}>>> = 2
    number_fluid_components<<<{"description": "The number of fluid components in the simulation"}>>> = 2
  []
  [pc]
    type = PorousFlowCapillaryPressureVG<<<{"description": "van Genuchten capillary pressure", "href": "../../../../source/userobjects/PorousFlowCapillaryPressureVG.html"}>>>
    m<<<{"description": "van Genuchten exponent m. Must be between 0 and 1, and optimally should be set to >0.5"}>>> = 0.5
    alpha<<<{"description": "van Genuchten parameter alpha. Must be positive"}>>> = 1
  []
[]

[FluidProperties<<<{"href": "../../../../syntax/FluidProperties/index.html"}>>>]
  [simple_fluid0]
    type = SimpleFluidProperties<<<{"description": "Fluid properties for a simple fluid with a constant bulk density", "href": "../../../../source/fluidproperties/SimpleFluidProperties.html"}>>>
    bulk_modulus<<<{"description": "Constant bulk modulus (Pa)"}>>> = 1.2
    density0<<<{"description": "Density at zero pressure and zero temperature"}>>> = 1
    viscosity<<<{"description": "Constant dynamic viscosity (Pa.s)"}>>> = 1
    thermal_expansion<<<{"description": "Constant coefficient of thermal expansion (1/K)"}>>> = 0
  []
  [simple_fluid1]
    type = SimpleFluidProperties<<<{"description": "Fluid properties for a simple fluid with a constant bulk density", "href": "../../../../source/fluidproperties/SimpleFluidProperties.html"}>>>
    bulk_modulus<<<{"description": "Constant bulk modulus (Pa)"}>>> = 1
    density0<<<{"description": "Density at zero pressure and zero temperature"}>>> = 0.1
    viscosity<<<{"description": "Constant dynamic viscosity (Pa.s)"}>>> = 0.5
    thermal_expansion<<<{"description": "Constant coefficient of thermal expansion (1/K)"}>>> = 0
  []
[]

[Materials<<<{"href": "../../../../syntax/Materials/index.html"}>>>]
  [temperature]
    type = PorousFlowTemperature<<<{"description": "Material to provide temperature at the quadpoints or nodes and derivatives of it with respect to the PorousFlow variables", "href": "../../../../source/materials/PorousFlowTemperature.html"}>>>
  []
  [ppss]
    type = PorousFlow2PhasePP<<<{"description": "This Material calculates the 2 porepressures and the 2 saturations in a 2-phase situation, and derivatives of these with respect to the PorousFlowVariables", "href": "../../../../source/materials/PorousFlow2PhasePP.html"}>>>
    phase0_porepressure<<<{"description": "Variable that is the porepressure of phase 0 (eg, the water phase).  It will be <= phase1_porepressure."}>>> = ppwater
    phase1_porepressure<<<{"description": "Variable that is the porepressure of phase 1 (eg, the gas phase)"}>>> = ppgas
    capillary_pressure<<<{"description": "Name of the UserObject defining the capillary pressure"}>>> = pc
  []
  [massfrac]
    type = PorousFlowMassFraction<<<{"description": "This Material forms a std::vector<std::vector ...> of mass-fractions out of the individual mass fractions", "href": "../../../../source/materials/PorousFlowMassFraction.html"}>>>
    mass_fraction_vars<<<{"description": "List of variables that represent the mass fractions.  Format is 'f_ph0^c0 f_ph0^c1 f_ph0^c2 ... f_ph0^c(N-2) f_ph1^c0 f_ph1^c1 fph1^c2 ... fph1^c(N-2) ... fphP^c0 f_phP^c1 fphP^c2 ... fphP^c(N-2)' where N=num_components and P=num_phases, and it is assumed that f_ph^c(N-1)=1-sum(f_ph^c,{c,0,N-2}) so that f_ph^c(N-1) need not be given.  If no variables are provided then num_phases=1=num_components."}>>> = 'massfrac_ph0_sp0 massfrac_ph1_sp0'
  []
  [simple_fluid0]
    type = PorousFlowSingleComponentFluid<<<{"description": "This Material calculates fluid properties at the quadpoints or nodes for a single component fluid", "href": "../../../../source/materials/PorousFlowSingleComponentFluid.html"}>>>
    fp<<<{"description": "The name of the user object for fluid properties"}>>> = simple_fluid0
    phase<<<{"description": "The phase number"}>>> = 0
  []
  [simple_fluid1]
    type = PorousFlowSingleComponentFluid<<<{"description": "This Material calculates fluid properties at the quadpoints or nodes for a single component fluid", "href": "../../../../source/materials/PorousFlowSingleComponentFluid.html"}>>>
    fp<<<{"description": "The name of the user object for fluid properties"}>>> = simple_fluid1
    phase<<<{"description": "The phase number"}>>> = 1
  []
  [porosity]
    type = PorousFlowPorosityConst<<<{"description": "This Material calculates the porosity assuming it is constant", "href": "../../../../source/materials/PorousFlowPorosityConst.html"}>>>
    porosity<<<{"description": "The porosity (assumed indepenent of porepressure, temperature, strain, etc, for this material).  This should be a real number, or a constant monomial variable (not a linear lagrange or other kind of variable)."}>>> = 0.1
  []
  [permeability]
    type = PorousFlowPermeabilityConst<<<{"description": "This Material calculates the permeability tensor assuming it is constant", "href": "../../../../source/materials/PorousFlowPermeabilityConst.html"}>>>
    permeability<<<{"description": "The permeability tensor (usually in m^2), which is assumed constant for this material"}>>> = '1 0 0  0 2 0  0 0 3'
  []
  [relperm_water]
    type = PorousFlowRelativePermeabilityCorey<<<{"description": "This Material calculates relative permeability of the fluid phase, using the simple Corey model ((S-S_res)/(1-sum(S_res)))^n", "href": "../../../../source/materials/PorousFlowRelativePermeabilityCorey.html"}>>>
    n<<<{"description": "The Corey exponent of the phase."}>>> = 1
    phase<<<{"description": "The phase number"}>>> = 0
  []
  [relperm_gas]
    type = PorousFlowRelativePermeabilityCorey<<<{"description": "This Material calculates relative permeability of the fluid phase, using the simple Corey model ((S-S_res)/(1-sum(S_res)))^n", "href": "../../../../source/materials/PorousFlowRelativePermeabilityCorey.html"}>>>
    n<<<{"description": "The Corey exponent of the phase."}>>> = 1
    phase<<<{"description": "The phase number"}>>> = 1
  []
[]

[Postprocessors<<<{"href": "../../../../syntax/Postprocessors/index.html"}>>>]
  [pp_water_top]
    type = PointValue<<<{"description": "Compute the value of a variable at a specified location", "href": "../../../../source/postprocessors/PointValue.html"}>>>
    variable<<<{"description": "The name of the variable that this postprocessor operates on."}>>> = ppwater
    point<<<{"description": "The physical point where the solution will be evaluated."}>>> = '0 0 0'
  []
  [pp_water_base]
    type = PointValue<<<{"description": "Compute the value of a variable at a specified location", "href": "../../../../source/postprocessors/PointValue.html"}>>>
    variable<<<{"description": "The name of the variable that this postprocessor operates on."}>>> = ppwater
    point<<<{"description": "The physical point where the solution will be evaluated."}>>> = '-1 0 0'
  []
  [pp_water_analytical]
    type = FunctionValuePostprocessor<<<{"description": "Computes the value of a supplied function at a single point (scalable)", "href": "../../../../source/postprocessors/FunctionValuePostprocessor.html"}>>>
    function<<<{"description": "The function which supplies the postprocessor value."}>>> = ana_ppwater
    point<<<{"description": "A set of three PostprocessorNames or constant values (or any mixture thereof) that will be passed to the function in the space argument"}>>> = '-1 0 0'
  []
  [ppwater_00]
    type = PointValue<<<{"description": "Compute the value of a variable at a specified location", "href": "../../../../source/postprocessors/PointValue.html"}>>>
    variable<<<{"description": "The name of the variable that this postprocessor operates on."}>>> = ppwater
    point<<<{"description": "The physical point where the solution will be evaluated."}>>> = '0 0 0'
  []
  [ppwater_01]
    type = PointValue<<<{"description": "Compute the value of a variable at a specified location", "href": "../../../../source/postprocessors/PointValue.html"}>>>
    variable<<<{"description": "The name of the variable that this postprocessor operates on."}>>> = ppwater
    point<<<{"description": "The physical point where the solution will be evaluated."}>>> = '-0.1 0 0'
  []
  [ppwater_02]
    type = PointValue<<<{"description": "Compute the value of a variable at a specified location", "href": "../../../../source/postprocessors/PointValue.html"}>>>
    variable<<<{"description": "The name of the variable that this postprocessor operates on."}>>> = ppwater
    point<<<{"description": "The physical point where the solution will be evaluated."}>>> = '-0.2 0 0'
  []
  [ppwater_03]
    type = PointValue<<<{"description": "Compute the value of a variable at a specified location", "href": "../../../../source/postprocessors/PointValue.html"}>>>
    variable<<<{"description": "The name of the variable that this postprocessor operates on."}>>> = ppwater
    point<<<{"description": "The physical point where the solution will be evaluated."}>>> = '-0.3 0 0'
  []
  [ppwater_04]
    type = PointValue<<<{"description": "Compute the value of a variable at a specified location", "href": "../../../../source/postprocessors/PointValue.html"}>>>
    variable<<<{"description": "The name of the variable that this postprocessor operates on."}>>> = ppwater
    point<<<{"description": "The physical point where the solution will be evaluated."}>>> = '-0.4 0 0'
  []
  [ppwater_05]
    type = PointValue<<<{"description": "Compute the value of a variable at a specified location", "href": "../../../../source/postprocessors/PointValue.html"}>>>
    variable<<<{"description": "The name of the variable that this postprocessor operates on."}>>> = ppwater
    point<<<{"description": "The physical point where the solution will be evaluated."}>>> = '-0.5 0 0'
  []
  [ppwater_06]
    type = PointValue<<<{"description": "Compute the value of a variable at a specified location", "href": "../../../../source/postprocessors/PointValue.html"}>>>
    variable<<<{"description": "The name of the variable that this postprocessor operates on."}>>> = ppwater
    point<<<{"description": "The physical point where the solution will be evaluated."}>>> = '-0.6 0 0'
  []
  [ppwater_07]
    type = PointValue<<<{"description": "Compute the value of a variable at a specified location", "href": "../../../../source/postprocessors/PointValue.html"}>>>
    variable<<<{"description": "The name of the variable that this postprocessor operates on."}>>> = ppwater
    point<<<{"description": "The physical point where the solution will be evaluated."}>>> = '-0.7 0 0'
  []
  [ppwater_08]
    type = PointValue<<<{"description": "Compute the value of a variable at a specified location", "href": "../../../../source/postprocessors/PointValue.html"}>>>
    variable<<<{"description": "The name of the variable that this postprocessor operates on."}>>> = ppwater
    point<<<{"description": "The physical point where the solution will be evaluated."}>>> = '-0.8 0 0'
  []
  [ppwater_09]
    type = PointValue<<<{"description": "Compute the value of a variable at a specified location", "href": "../../../../source/postprocessors/PointValue.html"}>>>
    variable<<<{"description": "The name of the variable that this postprocessor operates on."}>>> = ppwater
    point<<<{"description": "The physical point where the solution will be evaluated."}>>> = '-0.9 0 0'
  []
  [ppwater_10]
    type = PointValue<<<{"description": "Compute the value of a variable at a specified location", "href": "../../../../source/postprocessors/PointValue.html"}>>>
    variable<<<{"description": "The name of the variable that this postprocessor operates on."}>>> = ppwater
    point<<<{"description": "The physical point where the solution will be evaluated."}>>> = '-1 0 0'
  []
  [ppgas_00]
    type = PointValue<<<{"description": "Compute the value of a variable at a specified location", "href": "../../../../source/postprocessors/PointValue.html"}>>>
    variable<<<{"description": "The name of the variable that this postprocessor operates on."}>>> = ppgas
    point<<<{"description": "The physical point where the solution will be evaluated."}>>> = '0 0 0'
  []
  [ppgas_01]
    type = PointValue<<<{"description": "Compute the value of a variable at a specified location", "href": "../../../../source/postprocessors/PointValue.html"}>>>
    variable<<<{"description": "The name of the variable that this postprocessor operates on."}>>> = ppgas
    point<<<{"description": "The physical point where the solution will be evaluated."}>>> = '-0.1 0 0'
  []
  [ppgas_02]
    type = PointValue<<<{"description": "Compute the value of a variable at a specified location", "href": "../../../../source/postprocessors/PointValue.html"}>>>
    variable<<<{"description": "The name of the variable that this postprocessor operates on."}>>> = ppgas
    point<<<{"description": "The physical point where the solution will be evaluated."}>>> = '-0.2 0 0'
  []
  [ppgas_03]
    type = PointValue<<<{"description": "Compute the value of a variable at a specified location", "href": "../../../../source/postprocessors/PointValue.html"}>>>
    variable<<<{"description": "The name of the variable that this postprocessor operates on."}>>> = ppgas
    point<<<{"description": "The physical point where the solution will be evaluated."}>>> = '-0.3 0 0'
  []
  [ppgas_04]
    type = PointValue<<<{"description": "Compute the value of a variable at a specified location", "href": "../../../../source/postprocessors/PointValue.html"}>>>
    variable<<<{"description": "The name of the variable that this postprocessor operates on."}>>> = ppgas
    point<<<{"description": "The physical point where the solution will be evaluated."}>>> = '-0.4 0 0'
  []
  [ppgas_05]
    type = PointValue<<<{"description": "Compute the value of a variable at a specified location", "href": "../../../../source/postprocessors/PointValue.html"}>>>
    variable<<<{"description": "The name of the variable that this postprocessor operates on."}>>> = ppgas
    point<<<{"description": "The physical point where the solution will be evaluated."}>>> = '-0.5 0 0'
  []
  [ppgas_06]
    type = PointValue<<<{"description": "Compute the value of a variable at a specified location", "href": "../../../../source/postprocessors/PointValue.html"}>>>
    variable<<<{"description": "The name of the variable that this postprocessor operates on."}>>> = ppgas
    point<<<{"description": "The physical point where the solution will be evaluated."}>>> = '-0.6 0 0'
  []
  [ppgas_07]
    type = PointValue<<<{"description": "Compute the value of a variable at a specified location", "href": "../../../../source/postprocessors/PointValue.html"}>>>
    variable<<<{"description": "The name of the variable that this postprocessor operates on."}>>> = ppgas
    point<<<{"description": "The physical point where the solution will be evaluated."}>>> = '-0.7 0 0'
  []
  [ppgas_08]
    type = PointValue<<<{"description": "Compute the value of a variable at a specified location", "href": "../../../../source/postprocessors/PointValue.html"}>>>
    variable<<<{"description": "The name of the variable that this postprocessor operates on."}>>> = ppgas
    point<<<{"description": "The physical point where the solution will be evaluated."}>>> = '-0.8 0 0'
  []
  [ppgas_09]
    type = PointValue<<<{"description": "Compute the value of a variable at a specified location", "href": "../../../../source/postprocessors/PointValue.html"}>>>
    variable<<<{"description": "The name of the variable that this postprocessor operates on."}>>> = ppgas
    point<<<{"description": "The physical point where the solution will be evaluated."}>>> = '-0.9 0 0'
  []
  [ppgas_10]
    type = PointValue<<<{"description": "Compute the value of a variable at a specified location", "href": "../../../../source/postprocessors/PointValue.html"}>>>
    variable<<<{"description": "The name of the variable that this postprocessor operates on."}>>> = ppgas
    point<<<{"description": "The physical point where the solution will be evaluated."}>>> = '-1 0 0'
  []
[]

[Preconditioning<<<{"href": "../../../../syntax/Preconditioning/index.html"}>>>]
  active<<<{"description": "If specified only the blocks named will be visited and made active"}>>> = andy
  [andy]
    type = SMP<<<{"description": "Single matrix preconditioner (SMP) builds a preconditioner using user defined off-diagonal parts of the Jacobian.", "href": "../../../../source/preconditioners/SingleMatrixPreconditioner.html"}>>>
    full<<<{"description": "Set to true if you want the full set of couplings between variables simply for convenience so you don't have to set every off_diag_row and off_diag_column combination."}>>> = true
    petsc_options_iname<<<{"description": "Names of PETSc name/value pairs"}>>> = '-ksp_type -pc_type -snes_atol -snes_rtol -snes_max_it'
    petsc_options_value<<<{"description": "Values of PETSc name/value pairs (must correspond with \"petsc_options_iname\""}>>> = 'bcgs bjacobi 1E-12 1E-10 10000'
  []
  [check]
    type = SMP<<<{"description": "Single matrix preconditioner (SMP) builds a preconditioner using user defined off-diagonal parts of the Jacobian.", "href": "../../../../source/preconditioners/SingleMatrixPreconditioner.html"}>>>
    full<<<{"description": "Set to true if you want the full set of couplings between variables simply for convenience so you don't have to set every off_diag_row and off_diag_column combination."}>>> = true
    petsc_options_iname<<<{"description": "Names of PETSc name/value pairs"}>>> = '-ksp_type -pc_type -snes_atol -snes_rtol -snes_max_it -snes_type'
    petsc_options_value<<<{"description": "Values of PETSc name/value pairs (must correspond with \"petsc_options_iname\""}>>> = 'bcgs bjacobi 1E-12 1E-10 10000 test'
  []
[]

[Executioner<<<{"href": "../../../../syntax/Executioner/index.html"}>>>]
  type = Transient
  solve_type = Newton
  [TimeStepper<<<{"href": "../../../../syntax/Executioner/TimeStepper/index.html"}>>>]
    type = FunctionDT
    function = dts
  []
  end_time = 1.0
[]

[Outputs<<<{"href": "../../../../syntax/Outputs/index.html"}>>>]
  [csv]
    type = CSV<<<{"description": "Output for postprocessors, vector postprocessors, and scalar variables using comma seperated values (CSV).", "href": "../../../../source/outputs/CSV.html"}>>>
    execute_on<<<{"description": "The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html."}>>> = 'initial final'
    file_base<<<{"description": "The desired solution output name without an extension. If not provided, MOOSE sets it with Outputs/file_base when available. Otherwise, MOOSE uses input file name and this object name for a master input or uses master file_base, the subapp name and this object name for a subapp input to set it."}>>> = grav02d
  []
[]

Using the PS formulation with no residual saturation

# Checking that gravity head is established in the transient situation when 0<=saturation<=1 (note the less-than-or-equal-to).
# 2phase (PS), 2components, constant capillary pressure, constant fluid bulk-moduli for each phase, constant viscosity,
# constant permeability, Corey relative permeabilities with no residual saturation

[Mesh<<<{"href": "../../../../syntax/Mesh/index.html"}>>>]
  type = GeneratedMesh
  dim = 2
  ny = 10
  ymax = 100
[]

[GlobalParams<<<{"href": "../../../../syntax/GlobalParams/index.html"}>>>]
  PorousFlowDictator = dictator
  gravity = '0 -10 0'
[]

[Variables<<<{"href": "../../../../syntax/Variables/index.html"}>>>]
  [ppwater]
    initial_condition<<<{"description": "Specifies a constant initial condition for this variable"}>>> = 1.5e6
  []
  [sgas]
    initial_condition<<<{"description": "Specifies a constant initial condition for this variable"}>>> = 0.3
  []
[]

[AuxVariables<<<{"href": "../../../../syntax/AuxVariables/index.html"}>>>]
  [massfrac_ph0_sp0]
    initial_condition<<<{"description": "Specifies a constant initial condition for this variable"}>>> = 1
  []
  [massfrac_ph1_sp0]
    initial_condition<<<{"description": "Specifies a constant initial condition for this variable"}>>> = 0
  []
  [ppgas]
    family<<<{"description": "Specifies the family of FE shape functions to use for this variable"}>>> = MONOMIAL
    order<<<{"description": "Specifies the order of the FE shape function to use for this variable (additional orders not listed are allowed)"}>>> = FIRST
  []
  [swater]
    family<<<{"description": "Specifies the family of FE shape functions to use for this variable"}>>> = MONOMIAL
    order<<<{"description": "Specifies the order of the FE shape function to use for this variable (additional orders not listed are allowed)"}>>> = FIRST
  []
  [relpermwater]
    family<<<{"description": "Specifies the family of FE shape functions to use for this variable"}>>> = MONOMIAL
    order<<<{"description": "Specifies the order of the FE shape function to use for this variable (additional orders not listed are allowed)"}>>> = FIRST
  []
  [relpermgas]
    family<<<{"description": "Specifies the family of FE shape functions to use for this variable"}>>> = MONOMIAL
    order<<<{"description": "Specifies the order of the FE shape function to use for this variable (additional orders not listed are allowed)"}>>> = FIRST
  []
[]

[Kernels<<<{"href": "../../../../syntax/Kernels/index.html"}>>>]
  [mass0]
    type = PorousFlowMassTimeDerivative<<<{"description": "Derivative of fluid-component mass with respect to time.  Mass lumping to the nodes is used.", "href": "../../../../source/kernels/PorousFlowMassTimeDerivative.html"}>>>
    fluid_component<<<{"description": "The index corresponding to the component for this kernel"}>>> = 0
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = ppwater
  []
  [flux0]
    type = PorousFlowAdvectiveFlux<<<{"description": "Fully-upwinded advective flux of the component given by fluid_component", "href": "../../../../source/kernels/PorousFlowAdvectiveFlux.html"}>>>
    fluid_component<<<{"description": "The index corresponding to the fluid component for this kernel"}>>> = 0
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = ppwater
  []
  [mass1]
    type = PorousFlowMassTimeDerivative<<<{"description": "Derivative of fluid-component mass with respect to time.  Mass lumping to the nodes is used.", "href": "../../../../source/kernels/PorousFlowMassTimeDerivative.html"}>>>
    fluid_component<<<{"description": "The index corresponding to the component for this kernel"}>>> = 1
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = sgas
  []
  [flux1]
    type = PorousFlowAdvectiveFlux<<<{"description": "Fully-upwinded advective flux of the component given by fluid_component", "href": "../../../../source/kernels/PorousFlowAdvectiveFlux.html"}>>>
    fluid_component<<<{"description": "The index corresponding to the fluid component for this kernel"}>>> = 1
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = sgas
  []
[]

[AuxKernels<<<{"href": "../../../../syntax/AuxKernels/index.html"}>>>]
  [ppgas]
    type = PorousFlowPropertyAux<<<{"description": "AuxKernel to provide access to properties evaluated at quadpoints. Note that elemental AuxVariables must be used, so that these properties are integrated over each element.", "href": "../../../../source/auxkernels/PorousFlowPropertyAux.html"}>>>
    property<<<{"description": "The fluid property that this auxillary kernel is to calculate"}>>> = pressure
    phase<<<{"description": "The index of the phase this auxillary kernel acts on"}>>> = 1
    variable<<<{"description": "The name of the variable that this object applies to"}>>> = ppgas
  []
  [swater]
    type = PorousFlowPropertyAux<<<{"description": "AuxKernel to provide access to properties evaluated at quadpoints. Note that elemental AuxVariables must be used, so that these properties are integrated over each element.", "href": "../../../../source/auxkernels/PorousFlowPropertyAux.html"}>>>
    property<<<{"description": "The fluid property that this auxillary kernel is to calculate"}>>> = saturation
    phase<<<{"description": "The index of the phase this auxillary kernel acts on"}>>> = 0
    variable<<<{"description": "The name of the variable that this object applies to"}>>> = swater
  []
  [relpermwater]
    type = PorousFlowPropertyAux<<<{"description": "AuxKernel to provide access to properties evaluated at quadpoints. Note that elemental AuxVariables must be used, so that these properties are integrated over each element.", "href": "../../../../source/auxkernels/PorousFlowPropertyAux.html"}>>>
    property<<<{"description": "The fluid property that this auxillary kernel is to calculate"}>>> = relperm
    phase<<<{"description": "The index of the phase this auxillary kernel acts on"}>>> = 0
    variable<<<{"description": "The name of the variable that this object applies to"}>>> = relpermwater
  []
  [relpermgas]
    type = PorousFlowPropertyAux<<<{"description": "AuxKernel to provide access to properties evaluated at quadpoints. Note that elemental AuxVariables must be used, so that these properties are integrated over each element.", "href": "../../../../source/auxkernels/PorousFlowPropertyAux.html"}>>>
    property<<<{"description": "The fluid property that this auxillary kernel is to calculate"}>>> = relperm
    phase<<<{"description": "The index of the phase this auxillary kernel acts on"}>>> = 1
    variable<<<{"description": "The name of the variable that this object applies to"}>>> = relpermgas
  []
[]

[UserObjects<<<{"href": "../../../../syntax/UserObjects/index.html"}>>>]
  [dictator]
    type = PorousFlowDictator<<<{"description": "Holds information on the PorousFlow variable names", "href": "../../../../source/userobjects/PorousFlowDictator.html"}>>>
    porous_flow_vars<<<{"description": "List of primary variables that are used in the PorousFlow simulation.  Jacobian entries involving derivatives wrt these variables will be computed.  In single-phase models you will just have one (eg 'pressure'), in two-phase models you will have two (eg 'p_water p_gas', or 'p_water s_water'), etc."}>>> = 'ppwater sgas'
    number_fluid_phases<<<{"description": "The number of fluid phases in the simulation"}>>> = 2
    number_fluid_components<<<{"description": "The number of fluid components in the simulation"}>>> = 2
  []
  [pc]
    type = PorousFlowCapillaryPressureConst<<<{"description": "Constant capillary pressure", "href": "../../../../source/userobjects/PorousFlowCapillaryPressureConst.html"}>>>
    pc<<<{"description": "Constant capillary pressure (Pa). Default is 0"}>>> = 1e5
  []
[]

[FluidProperties<<<{"href": "../../../../syntax/FluidProperties/index.html"}>>>]
  [simple_fluid0]
    type = SimpleFluidProperties<<<{"description": "Fluid properties for a simple fluid with a constant bulk density", "href": "../../../../source/fluidproperties/SimpleFluidProperties.html"}>>>
    bulk_modulus<<<{"description": "Constant bulk modulus (Pa)"}>>> = 2e9
    density0<<<{"description": "Density at zero pressure and zero temperature"}>>> = 1000
    viscosity<<<{"description": "Constant dynamic viscosity (Pa.s)"}>>> = 1e-3
    thermal_expansion<<<{"description": "Constant coefficient of thermal expansion (1/K)"}>>> = 0
  []
  [simple_fluid1]
    type = SimpleFluidProperties<<<{"description": "Fluid properties for a simple fluid with a constant bulk density", "href": "../../../../source/fluidproperties/SimpleFluidProperties.html"}>>>
    bulk_modulus<<<{"description": "Constant bulk modulus (Pa)"}>>> = 2e9
    density0<<<{"description": "Density at zero pressure and zero temperature"}>>> = 10
    viscosity<<<{"description": "Constant dynamic viscosity (Pa.s)"}>>> = 1e-5
    thermal_expansion<<<{"description": "Constant coefficient of thermal expansion (1/K)"}>>> = 0
  []
[]

[Materials<<<{"href": "../../../../syntax/Materials/index.html"}>>>]
  [temperature]
    type = PorousFlowTemperature<<<{"description": "Material to provide temperature at the quadpoints or nodes and derivatives of it with respect to the PorousFlow variables", "href": "../../../../source/materials/PorousFlowTemperature.html"}>>>
  []
  [ppss]
    type = PorousFlow2PhasePS<<<{"description": "This Material calculates the 2 porepressures and the 2 saturations in a 2-phase situation, and derivatives of these with respect to the PorousFlowVariables.", "href": "../../../../source/materials/PorousFlow2PhasePS.html"}>>>
    phase0_porepressure<<<{"description": "Variable that is the porepressure of phase 0 (the liquid phase)"}>>> = ppwater
    phase1_saturation<<<{"description": "Variable that is the saturation of phase 1 (the gas phase)"}>>> = sgas
    capillary_pressure<<<{"description": "Name of the UserObject defining the capillary pressure"}>>> = pc
  []
  [massfrac]
    type = PorousFlowMassFraction<<<{"description": "This Material forms a std::vector<std::vector ...> of mass-fractions out of the individual mass fractions", "href": "../../../../source/materials/PorousFlowMassFraction.html"}>>>
    mass_fraction_vars<<<{"description": "List of variables that represent the mass fractions.  Format is 'f_ph0^c0 f_ph0^c1 f_ph0^c2 ... f_ph0^c(N-2) f_ph1^c0 f_ph1^c1 fph1^c2 ... fph1^c(N-2) ... fphP^c0 f_phP^c1 fphP^c2 ... fphP^c(N-2)' where N=num_components and P=num_phases, and it is assumed that f_ph^c(N-1)=1-sum(f_ph^c,{c,0,N-2}) so that f_ph^c(N-1) need not be given.  If no variables are provided then num_phases=1=num_components."}>>> = 'massfrac_ph0_sp0 massfrac_ph1_sp0'
  []
  [simple_fluid0]
    type = PorousFlowSingleComponentFluid<<<{"description": "This Material calculates fluid properties at the quadpoints or nodes for a single component fluid", "href": "../../../../source/materials/PorousFlowSingleComponentFluid.html"}>>>
    fp<<<{"description": "The name of the user object for fluid properties"}>>> = simple_fluid0
    phase<<<{"description": "The phase number"}>>> = 0
  []
  [simple_fluid1]
    type = PorousFlowSingleComponentFluid<<<{"description": "This Material calculates fluid properties at the quadpoints or nodes for a single component fluid", "href": "../../../../source/materials/PorousFlowSingleComponentFluid.html"}>>>
    fp<<<{"description": "The name of the user object for fluid properties"}>>> = simple_fluid1
    phase<<<{"description": "The phase number"}>>> = 1
  []
  [porosity]
    type = PorousFlowPorosityConst<<<{"description": "This Material calculates the porosity assuming it is constant", "href": "../../../../source/materials/PorousFlowPorosityConst.html"}>>>
    porosity<<<{"description": "The porosity (assumed indepenent of porepressure, temperature, strain, etc, for this material).  This should be a real number, or a constant monomial variable (not a linear lagrange or other kind of variable)."}>>> = 0.1
  []
  [permeability]
    type = PorousFlowPermeabilityConst<<<{"description": "This Material calculates the permeability tensor assuming it is constant", "href": "../../../../source/materials/PorousFlowPermeabilityConst.html"}>>>
    permeability<<<{"description": "The permeability tensor (usually in m^2), which is assumed constant for this material"}>>> = '1e-11 0 0 0 1e-11 0  0 0 1e-11'
  []
  [relperm_water]
    type = PorousFlowRelativePermeabilityCorey<<<{"description": "This Material calculates relative permeability of the fluid phase, using the simple Corey model ((S-S_res)/(1-sum(S_res)))^n", "href": "../../../../source/materials/PorousFlowRelativePermeabilityCorey.html"}>>>
    n<<<{"description": "The Corey exponent of the phase."}>>> = 2
    phase<<<{"description": "The phase number"}>>> = 0
  []
  [relperm_gas]
    type = PorousFlowRelativePermeabilityCorey<<<{"description": "This Material calculates relative permeability of the fluid phase, using the simple Corey model ((S-S_res)/(1-sum(S_res)))^n", "href": "../../../../source/materials/PorousFlowRelativePermeabilityCorey.html"}>>>
    n<<<{"description": "The Corey exponent of the phase."}>>> = 2
    phase<<<{"description": "The phase number"}>>> = 1
  []
[]

[Postprocessors<<<{"href": "../../../../syntax/Postprocessors/index.html"}>>>]
  [mass_ph0]
    type = PorousFlowFluidMass<<<{"description": "Calculates the mass of a fluid component in a region", "href": "../../../../source/postprocessors/PorousFlowFluidMass.html"}>>>
    fluid_component<<<{"description": "The index corresponding to the fluid component that this Postprocessor acts on"}>>> = 0
    execute_on<<<{"description": "The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html."}>>> = 'initial timestep_end'
  []
  [mass_ph1]
    type = PorousFlowFluidMass<<<{"description": "Calculates the mass of a fluid component in a region", "href": "../../../../source/postprocessors/PorousFlowFluidMass.html"}>>>
    fluid_component<<<{"description": "The index corresponding to the fluid component that this Postprocessor acts on"}>>> = 1
    execute_on<<<{"description": "The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html."}>>> = 'initial timestep_end'
  []
[]

[Preconditioning<<<{"href": "../../../../syntax/Preconditioning/index.html"}>>>]
  [smp]
    type = SMP<<<{"description": "Single matrix preconditioner (SMP) builds a preconditioner using user defined off-diagonal parts of the Jacobian.", "href": "../../../../source/preconditioners/SingleMatrixPreconditioner.html"}>>>
    full<<<{"description": "Set to true if you want the full set of couplings between variables simply for convenience so you don't have to set every off_diag_row and off_diag_column combination."}>>> = true
    petsc_options_iname<<<{"description": "Names of PETSc name/value pairs"}>>> = '-ksp_type -pc_type -snes_atol -snes_rtol'
    petsc_options_value<<<{"description": "Values of PETSc name/value pairs (must correspond with \"petsc_options_iname\""}>>> = 'bcgs bjacobi 1E-12 1E-10'
  []
[]

[Executioner<<<{"href": "../../../../syntax/Executioner/index.html"}>>>]
  type = Transient
  solve_type = Newton
  end_time = 1e5
  [TimeStepper<<<{"href": "../../../../syntax/Executioner/TimeStepper/index.html"}>>>]
    type = IterationAdaptiveDT
    dt = 1e4
  []
[]

[Outputs<<<{"href": "../../../../syntax/Outputs/index.html"}>>>]
  execute_on<<<{"description": "The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html."}>>> = 'initial timestep_end'
  file_base<<<{"description": "Common file base name to be utilized with all output objects"}>>> = grav02e
  exodus<<<{"description": "Output the results using the default settings for Exodus output."}>>> = true
  perf_graph<<<{"description": "Enable printing of the performance graph to the screen (Console)"}>>> = true
  csv<<<{"description": "Output the scalar variable and postprocessors to a *.csv file using the default CSV output."}>>> = false
[]

Using the PS formulation with residual saturation

# Checking that gravity head is established in the transient situation when 0<=saturation<=1 (note the less-than-or-equal-to).
# 2phase (PS), 2components, van Genuchten capillary pressure, constant fluid bulk-moduli for each phase, constant viscosity,
# constant permeability, Corey relative permeabilities with residual saturation

[Mesh<<<{"href": "../../../../syntax/Mesh/index.html"}>>>]
  type = GeneratedMesh
  dim = 2
  ny = 10
  ymax = 100
[]

[GlobalParams<<<{"href": "../../../../syntax/GlobalParams/index.html"}>>>]
  PorousFlowDictator = dictator
  gravity = '0 -10 0'
[]

[Variables<<<{"href": "../../../../syntax/Variables/index.html"}>>>]
  [ppwater]
    initial_condition<<<{"description": "Specifies a constant initial condition for this variable"}>>> = 1.5e6
  []
  [sgas]
    initial_condition<<<{"description": "Specifies a constant initial condition for this variable"}>>> = 0.3
  []
[]

[AuxVariables<<<{"href": "../../../../syntax/AuxVariables/index.html"}>>>]
  [massfrac_ph0_sp0]
    initial_condition<<<{"description": "Specifies a constant initial condition for this variable"}>>> = 1
  []
  [massfrac_ph1_sp0]
    initial_condition<<<{"description": "Specifies a constant initial condition for this variable"}>>> = 0
  []
  [ppgas]
    family<<<{"description": "Specifies the family of FE shape functions to use for this variable"}>>> = MONOMIAL
    order<<<{"description": "Specifies the order of the FE shape function to use for this variable (additional orders not listed are allowed)"}>>> = CONSTANT
  []
  [swater]
    family<<<{"description": "Specifies the family of FE shape functions to use for this variable"}>>> = MONOMIAL
    order<<<{"description": "Specifies the order of the FE shape function to use for this variable (additional orders not listed are allowed)"}>>> = CONSTANT
  []
  [relpermwater]
    family<<<{"description": "Specifies the family of FE shape functions to use for this variable"}>>> = MONOMIAL
    order<<<{"description": "Specifies the order of the FE shape function to use for this variable (additional orders not listed are allowed)"}>>> = CONSTANT
  []
  [relpermgas]
    family<<<{"description": "Specifies the family of FE shape functions to use for this variable"}>>> = MONOMIAL
    order<<<{"description": "Specifies the order of the FE shape function to use for this variable (additional orders not listed are allowed)"}>>> = CONSTANT
  []
[]

[Kernels<<<{"href": "../../../../syntax/Kernels/index.html"}>>>]
  [mass0]
    type = PorousFlowMassTimeDerivative<<<{"description": "Derivative of fluid-component mass with respect to time.  Mass lumping to the nodes is used.", "href": "../../../../source/kernels/PorousFlowMassTimeDerivative.html"}>>>
    fluid_component<<<{"description": "The index corresponding to the component for this kernel"}>>> = 0
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = ppwater
  []
  [flux0]
    type = PorousFlowAdvectiveFlux<<<{"description": "Fully-upwinded advective flux of the component given by fluid_component", "href": "../../../../source/kernels/PorousFlowAdvectiveFlux.html"}>>>
    fluid_component<<<{"description": "The index corresponding to the fluid component for this kernel"}>>> = 0
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = ppwater
  []
  [mass1]
    type = PorousFlowMassTimeDerivative<<<{"description": "Derivative of fluid-component mass with respect to time.  Mass lumping to the nodes is used.", "href": "../../../../source/kernels/PorousFlowMassTimeDerivative.html"}>>>
    fluid_component<<<{"description": "The index corresponding to the component for this kernel"}>>> = 1
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = sgas
  []
  [flux1]
    type = PorousFlowAdvectiveFlux<<<{"description": "Fully-upwinded advective flux of the component given by fluid_component", "href": "../../../../source/kernels/PorousFlowAdvectiveFlux.html"}>>>
    fluid_component<<<{"description": "The index corresponding to the fluid component for this kernel"}>>> = 1
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = sgas
  []
[]

[AuxKernels<<<{"href": "../../../../syntax/AuxKernels/index.html"}>>>]
  [ppgas]
    type = PorousFlowPropertyAux<<<{"description": "AuxKernel to provide access to properties evaluated at quadpoints. Note that elemental AuxVariables must be used, so that these properties are integrated over each element.", "href": "../../../../source/auxkernels/PorousFlowPropertyAux.html"}>>>
    property<<<{"description": "The fluid property that this auxillary kernel is to calculate"}>>> = pressure
    phase<<<{"description": "The index of the phase this auxillary kernel acts on"}>>> = 1
    variable<<<{"description": "The name of the variable that this object applies to"}>>> = ppgas
  []
  [swater]
    type = PorousFlowPropertyAux<<<{"description": "AuxKernel to provide access to properties evaluated at quadpoints. Note that elemental AuxVariables must be used, so that these properties are integrated over each element.", "href": "../../../../source/auxkernels/PorousFlowPropertyAux.html"}>>>
    property<<<{"description": "The fluid property that this auxillary kernel is to calculate"}>>> = saturation
    phase<<<{"description": "The index of the phase this auxillary kernel acts on"}>>> = 0
    variable<<<{"description": "The name of the variable that this object applies to"}>>> = swater
  []
  [relpermwater]
    type = MaterialStdVectorAux<<<{"description": "Extracts a component of a material type std::vector<Real> to an aux variable.  If the std::vector is not of sufficient size then zero is returned", "href": "../../../../source/auxkernels/MaterialStdVectorAux.html"}>>>
    property<<<{"description": "The material property name."}>>> = PorousFlow_relative_permeability_qp
    index<<<{"description": "The index to consider for this kernel"}>>> = 0
    variable<<<{"description": "The name of the variable that this object applies to"}>>> = relpermwater
  []
  [relpermgas]
    type = PorousFlowPropertyAux<<<{"description": "AuxKernel to provide access to properties evaluated at quadpoints. Note that elemental AuxVariables must be used, so that these properties are integrated over each element.", "href": "../../../../source/auxkernels/PorousFlowPropertyAux.html"}>>>
    property<<<{"description": "The fluid property that this auxillary kernel is to calculate"}>>> = relperm
    phase<<<{"description": "The index of the phase this auxillary kernel acts on"}>>> = 1
    variable<<<{"description": "The name of the variable that this object applies to"}>>> = relpermgas
  []
[]

[UserObjects<<<{"href": "../../../../syntax/UserObjects/index.html"}>>>]
  [dictator]
    type = PorousFlowDictator<<<{"description": "Holds information on the PorousFlow variable names", "href": "../../../../source/userobjects/PorousFlowDictator.html"}>>>
    porous_flow_vars<<<{"description": "List of primary variables that are used in the PorousFlow simulation.  Jacobian entries involving derivatives wrt these variables will be computed.  In single-phase models you will just have one (eg 'pressure'), in two-phase models you will have two (eg 'p_water p_gas', or 'p_water s_water'), etc."}>>> = 'ppwater sgas'
    number_fluid_phases<<<{"description": "The number of fluid phases in the simulation"}>>> = 2
    number_fluid_components<<<{"description": "The number of fluid components in the simulation"}>>> = 2
  []
  [pc]
    type = PorousFlowCapillaryPressureVG<<<{"description": "van Genuchten capillary pressure", "href": "../../../../source/userobjects/PorousFlowCapillaryPressureVG.html"}>>>
    m<<<{"description": "van Genuchten exponent m. Must be between 0 and 1, and optimally should be set to >0.5"}>>> = 0.5
    alpha<<<{"description": "van Genuchten parameter alpha. Must be positive"}>>> = 1e-4
    pc_max<<<{"description": "Maximum capillary pressure (Pa). Must be > 0. Default is 1e9"}>>> = 2e5
  []
[]

[FluidProperties<<<{"href": "../../../../syntax/FluidProperties/index.html"}>>>]
  [simple_fluid0]
    type = SimpleFluidProperties<<<{"description": "Fluid properties for a simple fluid with a constant bulk density", "href": "../../../../source/fluidproperties/SimpleFluidProperties.html"}>>>
    bulk_modulus<<<{"description": "Constant bulk modulus (Pa)"}>>> = 2e9
    density0<<<{"description": "Density at zero pressure and zero temperature"}>>> = 1000
    viscosity<<<{"description": "Constant dynamic viscosity (Pa.s)"}>>> = 1e-3
    thermal_expansion<<<{"description": "Constant coefficient of thermal expansion (1/K)"}>>> = 0
  []
  [simple_fluid1]
    type = SimpleFluidProperties<<<{"description": "Fluid properties for a simple fluid with a constant bulk density", "href": "../../../../source/fluidproperties/SimpleFluidProperties.html"}>>>
    bulk_modulus<<<{"description": "Constant bulk modulus (Pa)"}>>> = 2e9
    density0<<<{"description": "Density at zero pressure and zero temperature"}>>> = 10
    viscosity<<<{"description": "Constant dynamic viscosity (Pa.s)"}>>> = 1e-5
    thermal_expansion<<<{"description": "Constant coefficient of thermal expansion (1/K)"}>>> = 0
  []
[]

[Materials<<<{"href": "../../../../syntax/Materials/index.html"}>>>]
  [temperature]
    type = PorousFlowTemperature<<<{"description": "Material to provide temperature at the quadpoints or nodes and derivatives of it with respect to the PorousFlow variables", "href": "../../../../source/materials/PorousFlowTemperature.html"}>>>
  []
  [ppss]
    type = PorousFlow2PhasePS<<<{"description": "This Material calculates the 2 porepressures and the 2 saturations in a 2-phase situation, and derivatives of these with respect to the PorousFlowVariables.", "href": "../../../../source/materials/PorousFlow2PhasePS.html"}>>>
    phase0_porepressure<<<{"description": "Variable that is the porepressure of phase 0 (the liquid phase)"}>>> = ppwater
    phase1_saturation<<<{"description": "Variable that is the saturation of phase 1 (the gas phase)"}>>> = sgas
    capillary_pressure<<<{"description": "Name of the UserObject defining the capillary pressure"}>>> = pc
  []
  [massfrac]
    type = PorousFlowMassFraction<<<{"description": "This Material forms a std::vector<std::vector ...> of mass-fractions out of the individual mass fractions", "href": "../../../../source/materials/PorousFlowMassFraction.html"}>>>
    mass_fraction_vars<<<{"description": "List of variables that represent the mass fractions.  Format is 'f_ph0^c0 f_ph0^c1 f_ph0^c2 ... f_ph0^c(N-2) f_ph1^c0 f_ph1^c1 fph1^c2 ... fph1^c(N-2) ... fphP^c0 f_phP^c1 fphP^c2 ... fphP^c(N-2)' where N=num_components and P=num_phases, and it is assumed that f_ph^c(N-1)=1-sum(f_ph^c,{c,0,N-2}) so that f_ph^c(N-1) need not be given.  If no variables are provided then num_phases=1=num_components."}>>> = 'massfrac_ph0_sp0 massfrac_ph1_sp0'
  []
  [simple_fluid0]
    type = PorousFlowSingleComponentFluid<<<{"description": "This Material calculates fluid properties at the quadpoints or nodes for a single component fluid", "href": "../../../../source/materials/PorousFlowSingleComponentFluid.html"}>>>
    fp<<<{"description": "The name of the user object for fluid properties"}>>> = simple_fluid0
    phase<<<{"description": "The phase number"}>>> = 0
  []
  [simple_fluid1]
    type = PorousFlowSingleComponentFluid<<<{"description": "This Material calculates fluid properties at the quadpoints or nodes for a single component fluid", "href": "../../../../source/materials/PorousFlowSingleComponentFluid.html"}>>>
    fp<<<{"description": "The name of the user object for fluid properties"}>>> = simple_fluid1
    phase<<<{"description": "The phase number"}>>> = 1
  []
  [porosity]
    type = PorousFlowPorosityConst<<<{"description": "This Material calculates the porosity assuming it is constant", "href": "../../../../source/materials/PorousFlowPorosityConst.html"}>>>
    porosity<<<{"description": "The porosity (assumed indepenent of porepressure, temperature, strain, etc, for this material).  This should be a real number, or a constant monomial variable (not a linear lagrange or other kind of variable)."}>>> = 0.1
  []
  [permeability]
    type = PorousFlowPermeabilityConst<<<{"description": "This Material calculates the permeability tensor assuming it is constant", "href": "../../../../source/materials/PorousFlowPermeabilityConst.html"}>>>
    permeability<<<{"description": "The permeability tensor (usually in m^2), which is assumed constant for this material"}>>> = '1e-11 0 0 0 1e-11 0  0 0 1e-11'
  []
  [relperm_water]
    type = PorousFlowRelativePermeabilityCorey<<<{"description": "This Material calculates relative permeability of the fluid phase, using the simple Corey model ((S-S_res)/(1-sum(S_res)))^n", "href": "../../../../source/materials/PorousFlowRelativePermeabilityCorey.html"}>>>
    n<<<{"description": "The Corey exponent of the phase."}>>> = 2
    phase<<<{"description": "The phase number"}>>> = 0
    s_res<<<{"description": "The residual saturation of the phase j. Must be between 0 and 1"}>>> = 0.25
    sum_s_res<<<{"description": "Sum of residual saturations over all phases.  Must be between 0 and 1"}>>> = 0.35
  []
  [relperm_gas]
    type = PorousFlowRelativePermeabilityCorey<<<{"description": "This Material calculates relative permeability of the fluid phase, using the simple Corey model ((S-S_res)/(1-sum(S_res)))^n", "href": "../../../../source/materials/PorousFlowRelativePermeabilityCorey.html"}>>>
    n<<<{"description": "The Corey exponent of the phase."}>>> = 2
    phase<<<{"description": "The phase number"}>>> = 1
    s_res<<<{"description": "The residual saturation of the phase j. Must be between 0 and 1"}>>> = 0.1
    sum_s_res<<<{"description": "Sum of residual saturations over all phases.  Must be between 0 and 1"}>>> = 0.35
  []
[]

[Postprocessors<<<{"href": "../../../../syntax/Postprocessors/index.html"}>>>]
  [mass_ph0]
    type = PorousFlowFluidMass<<<{"description": "Calculates the mass of a fluid component in a region", "href": "../../../../source/postprocessors/PorousFlowFluidMass.html"}>>>
    fluid_component<<<{"description": "The index corresponding to the fluid component that this Postprocessor acts on"}>>> = 0
    execute_on<<<{"description": "The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html."}>>> = 'initial timestep_end'
  []
  [mass_ph1]
    type = PorousFlowFluidMass<<<{"description": "Calculates the mass of a fluid component in a region", "href": "../../../../source/postprocessors/PorousFlowFluidMass.html"}>>>
    fluid_component<<<{"description": "The index corresponding to the fluid component that this Postprocessor acts on"}>>> = 1
    execute_on<<<{"description": "The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html."}>>> = 'initial timestep_end'
  []
[]

[Preconditioning<<<{"href": "../../../../syntax/Preconditioning/index.html"}>>>]
  [smp]
    type = SMP<<<{"description": "Single matrix preconditioner (SMP) builds a preconditioner using user defined off-diagonal parts of the Jacobian.", "href": "../../../../source/preconditioners/SingleMatrixPreconditioner.html"}>>>
    full<<<{"description": "Set to true if you want the full set of couplings between variables simply for convenience so you don't have to set every off_diag_row and off_diag_column combination."}>>> = true
    petsc_options_iname<<<{"description": "Names of PETSc name/value pairs"}>>> = '-ksp_type -pc_type -snes_stol -snes_max_it'
    petsc_options_value<<<{"description": "Values of PETSc name/value pairs (must correspond with \"petsc_options_iname\""}>>> = 'bcgs bjacobi 1E-13 15'
  []
[]

[Executioner<<<{"href": "../../../../syntax/Executioner/index.html"}>>>]
  type = Transient
  solve_type = Newton
  end_time = 1e5
  [TimeStepper<<<{"href": "../../../../syntax/Executioner/TimeStepper/index.html"}>>>]
    type = IterationAdaptiveDT
    dt = 1e4
  []
[]

[Outputs<<<{"href": "../../../../syntax/Outputs/index.html"}>>>]
  execute_on<<<{"description": "The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html."}>>> = 'initial timestep_end'
  file_base<<<{"description": "Common file base name to be utilized with all output objects"}>>> = grav02f
  exodus<<<{"description": "Output the results using the default settings for Exodus output."}>>> = true
  perf_graph<<<{"description": "Enable printing of the performance graph to the screen (Console)"}>>> = true
  csv<<<{"description": "Output the scalar variable and postprocessors to a *.csv file using the default CSV output."}>>> = false
[]

Using the PS formulation with Brooks-Corey capillarity and residual saturation

# Checking that gravity head is established in the transient situation when 0<=saturation<=1 (note the less-than-or-equal-to).
# 2phase (PS), 2components, van Genuchten capillary pressure, constant fluid bulk-moduli for each phase, constant viscosity,
# constant permeability, Corey relative permeabilities with residual saturation

[Mesh<<<{"href": "../../../../syntax/Mesh/index.html"}>>>]
  type = GeneratedMesh
  dim = 2
  ny = 10
  ymax = 100
[]

[GlobalParams<<<{"href": "../../../../syntax/GlobalParams/index.html"}>>>]
  PorousFlowDictator = dictator
  gravity = '0 -10 0'
[]

[Variables<<<{"href": "../../../../syntax/Variables/index.html"}>>>]
  [ppwater]
    initial_condition<<<{"description": "Specifies a constant initial condition for this variable"}>>> = 1.5e6
  []
  [sgas]
    initial_condition<<<{"description": "Specifies a constant initial condition for this variable"}>>> = 0.3
  []
[]

[AuxVariables<<<{"href": "../../../../syntax/AuxVariables/index.html"}>>>]
  [massfrac_ph0_sp0]
    initial_condition<<<{"description": "Specifies a constant initial condition for this variable"}>>> = 1
  []
  [massfrac_ph1_sp0]
    initial_condition<<<{"description": "Specifies a constant initial condition for this variable"}>>> = 0
  []
  [ppgas]
    family<<<{"description": "Specifies the family of FE shape functions to use for this variable"}>>> = MONOMIAL
    order<<<{"description": "Specifies the order of the FE shape function to use for this variable (additional orders not listed are allowed)"}>>> = CONSTANT
  []
  [swater]
    family<<<{"description": "Specifies the family of FE shape functions to use for this variable"}>>> = MONOMIAL
    order<<<{"description": "Specifies the order of the FE shape function to use for this variable (additional orders not listed are allowed)"}>>> = CONSTANT
  []
  [relpermwater]
    family<<<{"description": "Specifies the family of FE shape functions to use for this variable"}>>> = MONOMIAL
    order<<<{"description": "Specifies the order of the FE shape function to use for this variable (additional orders not listed are allowed)"}>>> = CONSTANT
  []
  [relpermgas]
    family<<<{"description": "Specifies the family of FE shape functions to use for this variable"}>>> = MONOMIAL
    order<<<{"description": "Specifies the order of the FE shape function to use for this variable (additional orders not listed are allowed)"}>>> = CONSTANT
  []
[]

[Kernels<<<{"href": "../../../../syntax/Kernels/index.html"}>>>]
  [mass0]
    type = PorousFlowMassTimeDerivative<<<{"description": "Derivative of fluid-component mass with respect to time.  Mass lumping to the nodes is used.", "href": "../../../../source/kernels/PorousFlowMassTimeDerivative.html"}>>>
    fluid_component<<<{"description": "The index corresponding to the component for this kernel"}>>> = 0
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = ppwater
  []
  [flux0]
    type = PorousFlowAdvectiveFlux<<<{"description": "Fully-upwinded advective flux of the component given by fluid_component", "href": "../../../../source/kernels/PorousFlowAdvectiveFlux.html"}>>>
    fluid_component<<<{"description": "The index corresponding to the fluid component for this kernel"}>>> = 0
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = ppwater
  []
  [mass1]
    type = PorousFlowMassTimeDerivative<<<{"description": "Derivative of fluid-component mass with respect to time.  Mass lumping to the nodes is used.", "href": "../../../../source/kernels/PorousFlowMassTimeDerivative.html"}>>>
    fluid_component<<<{"description": "The index corresponding to the component for this kernel"}>>> = 1
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = sgas
  []
  [flux1]
    type = PorousFlowAdvectiveFlux<<<{"description": "Fully-upwinded advective flux of the component given by fluid_component", "href": "../../../../source/kernels/PorousFlowAdvectiveFlux.html"}>>>
    fluid_component<<<{"description": "The index corresponding to the fluid component for this kernel"}>>> = 1
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = sgas
  []
[]

[AuxKernels<<<{"href": "../../../../syntax/AuxKernels/index.html"}>>>]
  [ppgas]
    type = PorousFlowPropertyAux<<<{"description": "AuxKernel to provide access to properties evaluated at quadpoints. Note that elemental AuxVariables must be used, so that these properties are integrated over each element.", "href": "../../../../source/auxkernels/PorousFlowPropertyAux.html"}>>>
    property<<<{"description": "The fluid property that this auxillary kernel is to calculate"}>>> = pressure
    phase<<<{"description": "The index of the phase this auxillary kernel acts on"}>>> = 1
    variable<<<{"description": "The name of the variable that this object applies to"}>>> = ppgas
  []
  [swater]
    type = PorousFlowPropertyAux<<<{"description": "AuxKernel to provide access to properties evaluated at quadpoints. Note that elemental AuxVariables must be used, so that these properties are integrated over each element.", "href": "../../../../source/auxkernels/PorousFlowPropertyAux.html"}>>>
    property<<<{"description": "The fluid property that this auxillary kernel is to calculate"}>>> = saturation
    phase<<<{"description": "The index of the phase this auxillary kernel acts on"}>>> = 0
    variable<<<{"description": "The name of the variable that this object applies to"}>>> = swater
  []
  [relpermwater]
    type = MaterialStdVectorAux<<<{"description": "Extracts a component of a material type std::vector<Real> to an aux variable.  If the std::vector is not of sufficient size then zero is returned", "href": "../../../../source/auxkernels/MaterialStdVectorAux.html"}>>>
    property<<<{"description": "The material property name."}>>> = PorousFlow_relative_permeability_qp
    index<<<{"description": "The index to consider for this kernel"}>>> = 0
    variable<<<{"description": "The name of the variable that this object applies to"}>>> = relpermwater
  []
  [relpermgas]
    type = PorousFlowPropertyAux<<<{"description": "AuxKernel to provide access to properties evaluated at quadpoints. Note that elemental AuxVariables must be used, so that these properties are integrated over each element.", "href": "../../../../source/auxkernels/PorousFlowPropertyAux.html"}>>>
    property<<<{"description": "The fluid property that this auxillary kernel is to calculate"}>>> = relperm
    phase<<<{"description": "The index of the phase this auxillary kernel acts on"}>>> = 1
    variable<<<{"description": "The name of the variable that this object applies to"}>>> = relpermgas
  []
[]

[UserObjects<<<{"href": "../../../../syntax/UserObjects/index.html"}>>>]
  [dictator]
    type = PorousFlowDictator<<<{"description": "Holds information on the PorousFlow variable names", "href": "../../../../source/userobjects/PorousFlowDictator.html"}>>>
    porous_flow_vars<<<{"description": "List of primary variables that are used in the PorousFlow simulation.  Jacobian entries involving derivatives wrt these variables will be computed.  In single-phase models you will just have one (eg 'pressure'), in two-phase models you will have two (eg 'p_water p_gas', or 'p_water s_water'), etc."}>>> = 'ppwater sgas'
    number_fluid_phases<<<{"description": "The number of fluid phases in the simulation"}>>> = 2
    number_fluid_components<<<{"description": "The number of fluid components in the simulation"}>>> = 2
  []
  [pc]
    type = PorousFlowCapillaryPressureVG<<<{"description": "van Genuchten capillary pressure", "href": "../../../../source/userobjects/PorousFlowCapillaryPressureVG.html"}>>>
    m<<<{"description": "van Genuchten exponent m. Must be between 0 and 1, and optimally should be set to >0.5"}>>> = 0.5
    alpha<<<{"description": "van Genuchten parameter alpha. Must be positive"}>>> = 1e-4
    pc_max<<<{"description": "Maximum capillary pressure (Pa). Must be > 0. Default is 1e9"}>>> = 2e5
  []
[]

[FluidProperties<<<{"href": "../../../../syntax/FluidProperties/index.html"}>>>]
  [simple_fluid0]
    type = SimpleFluidProperties<<<{"description": "Fluid properties for a simple fluid with a constant bulk density", "href": "../../../../source/fluidproperties/SimpleFluidProperties.html"}>>>
    bulk_modulus<<<{"description": "Constant bulk modulus (Pa)"}>>> = 2e9
    density0<<<{"description": "Density at zero pressure and zero temperature"}>>> = 1000
    viscosity<<<{"description": "Constant dynamic viscosity (Pa.s)"}>>> = 1e-3
    thermal_expansion<<<{"description": "Constant coefficient of thermal expansion (1/K)"}>>> = 0
  []
  [simple_fluid1]
    type = SimpleFluidProperties<<<{"description": "Fluid properties for a simple fluid with a constant bulk density", "href": "../../../../source/fluidproperties/SimpleFluidProperties.html"}>>>
    bulk_modulus<<<{"description": "Constant bulk modulus (Pa)"}>>> = 2e9
    density0<<<{"description": "Density at zero pressure and zero temperature"}>>> = 10
    viscosity<<<{"description": "Constant dynamic viscosity (Pa.s)"}>>> = 1e-5
    thermal_expansion<<<{"description": "Constant coefficient of thermal expansion (1/K)"}>>> = 0
  []
[]

[Materials<<<{"href": "../../../../syntax/Materials/index.html"}>>>]
  [temperature]
    type = PorousFlowTemperature<<<{"description": "Material to provide temperature at the quadpoints or nodes and derivatives of it with respect to the PorousFlow variables", "href": "../../../../source/materials/PorousFlowTemperature.html"}>>>
  []
  [ppss]
    type = PorousFlow2PhasePS<<<{"description": "This Material calculates the 2 porepressures and the 2 saturations in a 2-phase situation, and derivatives of these with respect to the PorousFlowVariables.", "href": "../../../../source/materials/PorousFlow2PhasePS.html"}>>>
    phase0_porepressure<<<{"description": "Variable that is the porepressure of phase 0 (the liquid phase)"}>>> = ppwater
    phase1_saturation<<<{"description": "Variable that is the saturation of phase 1 (the gas phase)"}>>> = sgas
    capillary_pressure<<<{"description": "Name of the UserObject defining the capillary pressure"}>>> = pc
  []
  [massfrac]
    type = PorousFlowMassFraction<<<{"description": "This Material forms a std::vector<std::vector ...> of mass-fractions out of the individual mass fractions", "href": "../../../../source/materials/PorousFlowMassFraction.html"}>>>
    mass_fraction_vars<<<{"description": "List of variables that represent the mass fractions.  Format is 'f_ph0^c0 f_ph0^c1 f_ph0^c2 ... f_ph0^c(N-2) f_ph1^c0 f_ph1^c1 fph1^c2 ... fph1^c(N-2) ... fphP^c0 f_phP^c1 fphP^c2 ... fphP^c(N-2)' where N=num_components and P=num_phases, and it is assumed that f_ph^c(N-1)=1-sum(f_ph^c,{c,0,N-2}) so that f_ph^c(N-1) need not be given.  If no variables are provided then num_phases=1=num_components."}>>> = 'massfrac_ph0_sp0 massfrac_ph1_sp0'
  []
  [simple_fluid0]
    type = PorousFlowSingleComponentFluid<<<{"description": "This Material calculates fluid properties at the quadpoints or nodes for a single component fluid", "href": "../../../../source/materials/PorousFlowSingleComponentFluid.html"}>>>
    fp<<<{"description": "The name of the user object for fluid properties"}>>> = simple_fluid0
    phase<<<{"description": "The phase number"}>>> = 0
  []
  [simple_fluid1]
    type = PorousFlowSingleComponentFluid<<<{"description": "This Material calculates fluid properties at the quadpoints or nodes for a single component fluid", "href": "../../../../source/materials/PorousFlowSingleComponentFluid.html"}>>>
    fp<<<{"description": "The name of the user object for fluid properties"}>>> = simple_fluid1
    phase<<<{"description": "The phase number"}>>> = 1
  []
  [porosity]
    type = PorousFlowPorosityConst<<<{"description": "This Material calculates the porosity assuming it is constant", "href": "../../../../source/materials/PorousFlowPorosityConst.html"}>>>
    porosity<<<{"description": "The porosity (assumed indepenent of porepressure, temperature, strain, etc, for this material).  This should be a real number, or a constant monomial variable (not a linear lagrange or other kind of variable)."}>>> = 0.1
  []
  [permeability]
    type = PorousFlowPermeabilityConst<<<{"description": "This Material calculates the permeability tensor assuming it is constant", "href": "../../../../source/materials/PorousFlowPermeabilityConst.html"}>>>
    permeability<<<{"description": "The permeability tensor (usually in m^2), which is assumed constant for this material"}>>> = '1e-11 0 0 0 1e-11 0  0 0 1e-11'
  []
  [relperm_water]
    type = PorousFlowRelativePermeabilityCorey<<<{"description": "This Material calculates relative permeability of the fluid phase, using the simple Corey model ((S-S_res)/(1-sum(S_res)))^n", "href": "../../../../source/materials/PorousFlowRelativePermeabilityCorey.html"}>>>
    n<<<{"description": "The Corey exponent of the phase."}>>> = 2
    phase<<<{"description": "The phase number"}>>> = 0
    s_res<<<{"description": "The residual saturation of the phase j. Must be between 0 and 1"}>>> = 0.25
    sum_s_res<<<{"description": "Sum of residual saturations over all phases.  Must be between 0 and 1"}>>> = 0.35
  []
  [relperm_gas]
    type = PorousFlowRelativePermeabilityCorey<<<{"description": "This Material calculates relative permeability of the fluid phase, using the simple Corey model ((S-S_res)/(1-sum(S_res)))^n", "href": "../../../../source/materials/PorousFlowRelativePermeabilityCorey.html"}>>>
    n<<<{"description": "The Corey exponent of the phase."}>>> = 2
    phase<<<{"description": "The phase number"}>>> = 1
    s_res<<<{"description": "The residual saturation of the phase j. Must be between 0 and 1"}>>> = 0.1
    sum_s_res<<<{"description": "Sum of residual saturations over all phases.  Must be between 0 and 1"}>>> = 0.35
  []
[]

[Postprocessors<<<{"href": "../../../../syntax/Postprocessors/index.html"}>>>]
  [mass_ph0]
    type = PorousFlowFluidMass<<<{"description": "Calculates the mass of a fluid component in a region", "href": "../../../../source/postprocessors/PorousFlowFluidMass.html"}>>>
    fluid_component<<<{"description": "The index corresponding to the fluid component that this Postprocessor acts on"}>>> = 0
    execute_on<<<{"description": "The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html."}>>> = 'initial timestep_end'
  []
  [mass_ph1]
    type = PorousFlowFluidMass<<<{"description": "Calculates the mass of a fluid component in a region", "href": "../../../../source/postprocessors/PorousFlowFluidMass.html"}>>>
    fluid_component<<<{"description": "The index corresponding to the fluid component that this Postprocessor acts on"}>>> = 1
    execute_on<<<{"description": "The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html."}>>> = 'initial timestep_end'
  []
[]

[Preconditioning<<<{"href": "../../../../syntax/Preconditioning/index.html"}>>>]
  [smp]
    type = SMP<<<{"description": "Single matrix preconditioner (SMP) builds a preconditioner using user defined off-diagonal parts of the Jacobian.", "href": "../../../../source/preconditioners/SingleMatrixPreconditioner.html"}>>>
    full<<<{"description": "Set to true if you want the full set of couplings between variables simply for convenience so you don't have to set every off_diag_row and off_diag_column combination."}>>> = true
    petsc_options_iname<<<{"description": "Names of PETSc name/value pairs"}>>> = '-ksp_type -pc_type -snes_stol -snes_max_it'
    petsc_options_value<<<{"description": "Values of PETSc name/value pairs (must correspond with \"petsc_options_iname\""}>>> = 'bcgs bjacobi 1E-13 15'
  []
[]

[Executioner<<<{"href": "../../../../syntax/Executioner/index.html"}>>>]
  type = Transient
  solve_type = Newton
  end_time = 1e5
  [TimeStepper<<<{"href": "../../../../syntax/Executioner/TimeStepper/index.html"}>>>]
    type = IterationAdaptiveDT
    dt = 1e4
  []
[]

[Outputs<<<{"href": "../../../../syntax/Outputs/index.html"}>>>]
  execute_on<<<{"description": "The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html."}>>> = 'initial timestep_end'
  file_base<<<{"description": "Common file base name to be utilized with all output objects"}>>> = grav02f
  exodus<<<{"description": "Output the results using the default settings for Exodus output."}>>> = true
  perf_graph<<<{"description": "Enable printing of the performance graph to the screen (Console)"}>>> = true
  csv<<<{"description": "Output the scalar variable and postprocessors to a *.csv file using the default CSV output."}>>> = false
[]

(modules/porous_flow/test/tests/gravity/grav01a.i)

# Checking that gravity head is established
# 1phase, vanGenuchten, constant fluid-bulk, constant viscosity, constant permeability, Corey relative perm
# fully saturated
# For better agreement with the analytical solution (ana_pp), just increase nx

[Mesh]
  type = GeneratedMesh
  dim = 1
  nx = 100
  xmin = -1
  xmax = 0
[]

[GlobalParams]
  PorousFlowDictator = dictator
[]

[Variables]
  [pp]
    [InitialCondition]
      type = RandomIC
      min = 0
      max = 1
    []
  []
[]

[Kernels]
  [flux0]
    type = PorousFlowAdvectiveFlux
    fluid_component = 0
    variable = pp
    gravity = '-1 0 0'
  []
[]

[Functions]
  [ana_pp]
    type = ParsedFunction
    symbol_names = 'g B p0 rho0'
    symbol_values = '1 1.2 0 1'
    expression = '-B*log(exp(-p0/B)+g*rho0*x/B)' # expected pp at base
  []
[]

[BCs]
  [z]
    type = DirichletBC
    variable = pp
    boundary = right
    value = 0
  []
[]

[UserObjects]
  [dictator]
    type = PorousFlowDictator
    porous_flow_vars = 'pp'
    number_fluid_phases = 1
    number_fluid_components = 1
  []
  [pc]
    type = PorousFlowCapillaryPressureVG
    m = 0.5
    alpha = 1
  []
[]

[FluidProperties]
  [simple_fluid]
    type = SimpleFluidProperties
    bulk_modulus = 1.2
    density0 = 1
    viscosity = 1
    thermal_expansion = 0
  []
[]

[Materials]
  [temperature]
    type = PorousFlowTemperature
  []
  [ppss]
    type = PorousFlow1PhaseP
    porepressure = pp
    capillary_pressure = pc
  []
  [massfrac]
    type = PorousFlowMassFraction
  []
  [simple_fluid]
    type = PorousFlowSingleComponentFluid
    fp = simple_fluid
    phase = 0
  []
  [permeability]
    type = PorousFlowPermeabilityConst
    permeability = '1 0 0  0 2 0  0 0 3'
  []
  [relperm]
    type = PorousFlowRelativePermeabilityCorey
    n = 1
    phase = 0
  []
[]

[Postprocessors]
  [pp_base]
    type = PointValue
    variable = pp
    point = '-1 0 0'
  []
  [pp_analytical]
    type = FunctionValuePostprocessor
    function = ana_pp
    point = '-1 0 0'
  []
  [pp_00]
    type = PointValue
    variable = pp
    point = '0 0 0'
  []
  [pp_01]
    type = PointValue
    variable = pp
    point = '-0.1 0 0'
  []
  [pp_02]
    type = PointValue
    variable = pp
    point = '-0.2 0 0'
  []
  [pp_03]
    type = PointValue
    variable = pp
    point = '-0.3 0 0'
  []
  [pp_04]
    type = PointValue
    variable = pp
    point = '-0.4 0 0'
  []
  [pp_05]
    type = PointValue
    variable = pp
    point = '-0.5 0 0'
  []
  [pp_06]
    type = PointValue
    variable = pp
    point = '-0.6 0 0'
  []
  [pp_07]
    type = PointValue
    variable = pp
    point = '-0.7 0 0'
  []
  [pp_08]
    type = PointValue
    variable = pp
    point = '-0.8 0 0'
  []
  [pp_09]
    type = PointValue
    variable = pp
    point = '-0.9 0 0'
  []
  [pp_10]
    type = PointValue
    variable = pp
    point = '-1 0 0'
  []
[]

[Preconditioning]
  [andy]
    type = SMP
    full = true
  []
[]

[Executioner]
  type = Steady
  solve_type = Newton
[]

[Outputs]
  execute_on = 'timestep_end'
  file_base = grav01a
  [csv]
    type = CSV
  []
[]

(modules/porous_flow/test/tests/gravity/grav01c.i)

# Checking that gravity head is established
# 1phase, vanGenuchten, constant fluid-bulk, constant viscosity, constant permeability, Corey relative perm
# unsaturated
# For better agreement with the analytical solution (ana_pp), just increase nx

[Mesh]
  type = GeneratedMesh
  dim = 1
  nx = 100
  xmin = -1
  xmax = 0
[]

[GlobalParams]
  PorousFlowDictator = dictator
[]

[Variables]
  [pp]
    [InitialCondition]
      type = RandomIC
      min = -1
      max = 1
    []
  []
[]

[Kernels]
  [flux0]
    type = PorousFlowAdvectiveFlux
    fluid_component = 0
    variable = pp
    gravity = '-1 0 0'
  []
[]

[Functions]
  [ana_pp]
    type = ParsedFunction
    symbol_names = 'g B p0 rho0'
    symbol_values = '1 2 -1 1'
    expression = '-B*log(exp(-p0/B)+g*rho0*x/B)' # expected pp at base
  []
[]

[BCs]
  [z]
    type = DirichletBC
    variable = pp
    boundary = right
    value = -1
  []
[]

[UserObjects]
  [dictator]
    type = PorousFlowDictator
    porous_flow_vars = 'pp'
    number_fluid_phases = 1
    number_fluid_components = 1
  []
  [pc]
    type = PorousFlowCapillaryPressureVG
    m = 0.5
    alpha = 1
  []
[]

[FluidProperties]
  [simple_fluid]
    type = SimpleFluidProperties
    bulk_modulus = 2
    density0 = 1
    viscosity = 1
    thermal_expansion = 0
  []
[]

[Materials]
  [temperature]
    type = PorousFlowTemperature
  []
  [ppss]
    type = PorousFlow1PhaseP
    porepressure = pp
    capillary_pressure = pc
  []
  [massfrac]
    type = PorousFlowMassFraction
  []
  [simple_fluid]
    type = PorousFlowSingleComponentFluid
    fp = simple_fluid
    phase = 0
  []
  [permeability]
    type = PorousFlowPermeabilityConst
    permeability = '1 0 0  0 2 0  0 0 3'
  []
  [relperm]
    type = PorousFlowRelativePermeabilityCorey
    n = 1
    phase = 0
  []
[]

[Postprocessors]
  [pp_base]
    type = PointValue
    variable = pp
    point = '-1 0 0'
  []
  [pp_analytical]
    type = FunctionValuePostprocessor
    function = ana_pp
    point = '-1 0 0'
  []
[]

[Preconditioning]
  [andy]
    type = SMP
    full = true
  []
[]

[Executioner]
  type = Steady
  solve_type = Newton
[]

[Outputs]
  execute_on = 'timestep_end'
  file_base = grav01c
  exodus = true
  [csv]
    type = CSV
  []
[]

(modules/porous_flow/test/tests/gravity/grav02b.i)

# Checking that gravity head is established in the steady-state situation when 0<saturation<1 (note the strictly less-than).
# 2phase (PP), 2components, vanGenuchten, constant fluid bulk-moduli for each phase, constant viscosity, constant permeability, Corey relative perm
# For better agreement with the analytical solution (ana_pp), just increase nx

[Mesh]
  type = GeneratedMesh
  dim = 1
  nx = 10
  xmin = -1
  xmax = 0
[]

[GlobalParams]
  PorousFlowDictator = dictator
[]

[Variables]
  [ppwater]
    initial_condition = -1.0
  []
  [ppgas]
    initial_condition = 0
  []
[]

[AuxVariables]
  [massfrac_ph0_sp0]
    initial_condition = 1
  []
  [massfrac_ph1_sp0]
    initial_condition = 0
  []
[]

[Kernels]
  [flux0]
    type = PorousFlowAdvectiveFlux
    fluid_component = 0
    variable = ppwater
    gravity = '-1 0 0'
  []
  [flux1]
    type = PorousFlowAdvectiveFlux
    fluid_component = 1
    variable = ppgas
    gravity = '-1 0 0'
  []
[]

[BCs]
  [ppwater]
    type = DirichletBC
    boundary = right
    variable = ppwater
    value = -1
  []
  [ppgas]
    type = DirichletBC
    boundary = right
    variable = ppgas
    value = 0
  []
[]

[Functions]
  [ana_ppwater]
    type = ParsedFunction
    symbol_names = 'g B p0 rho0'
    symbol_values = '1 2 pp_water_top 1'
    expression = '-B*log(exp(-p0/B)+g*rho0*x/B)' # expected pp at base
  []
  [ana_ppgas]
    type = ParsedFunction
    symbol_names = 'g B p0 rho0'
    symbol_values = '1 1 pp_gas_top 0.1'
    expression = '-B*log(exp(-p0/B)+g*rho0*x/B)' # expected pp at base
  []
[]

[UserObjects]
  [dictator]
    type = PorousFlowDictator
    porous_flow_vars = 'ppwater ppgas'
    number_fluid_phases = 2
    number_fluid_components = 2
  []
  [pc]
    type = PorousFlowCapillaryPressureVG
    m = 0.5
    alpha = 1
  []
[]

[FluidProperties]
  [simple_fluid0]
    type = SimpleFluidProperties
    bulk_modulus = 2
    density0 = 1
    viscosity = 1
    thermal_expansion = 0
  []
  [simple_fluid1]
    type = SimpleFluidProperties
    bulk_modulus = 1
    density0 = 0.1
    viscosity = 0.5
    thermal_expansion = 0
  []
[]

[Materials]
  [temperature]
    type = PorousFlowTemperature
  []
  [ppss]
    type = PorousFlow2PhasePP
    phase0_porepressure = ppwater
    phase1_porepressure = ppgas
    capillary_pressure = pc
  []
  [massfrac]
    type = PorousFlowMassFraction
    mass_fraction_vars = 'massfrac_ph0_sp0 massfrac_ph1_sp0'
  []
  [simple_fluid0]
    type = PorousFlowSingleComponentFluid
    fp = simple_fluid0
    phase = 0
  []
  [simple_fluid1]
    type = PorousFlowSingleComponentFluid
    fp = simple_fluid1
    phase = 1
  []
  [permeability]
    type = PorousFlowPermeabilityConst
    permeability = '1 0 0  0 2 0  0 0 3'
  []
  [relperm_water]
    type = PorousFlowRelativePermeabilityCorey
    n = 1
    phase = 0
  []
  [relperm_gas]
    type = PorousFlowRelativePermeabilityCorey
    n = 1
    phase = 1
  []
[]

[Postprocessors]
  [pp_water_top]
    type = PointValue
    variable = ppwater
    point = '0 0 0'
  []
  [pp_water_base]
    type = PointValue
    variable = ppwater
    point = '-1 0 0'
  []
  [pp_water_analytical]
    type = FunctionValuePostprocessor
    function = ana_ppwater
    point = '-1 0 0'
  []
  [pp_gas_top]
    type = PointValue
    variable = ppgas
    point = '0 0 0'
  []
  [pp_gas_base]
    type = PointValue
    variable = ppgas
    point = '-1 0 0'
  []
  [pp_gas_analytical]
    type = FunctionValuePostprocessor
    function = ana_ppgas
    point = '-1 0 0'
  []
[]

[Preconditioning]
  [andy]
    type = SMP
    full = true
  []
[]


[Executioner]
  type = Steady
  solve_type = Newton
[]

[Outputs]
  file_base = grav02b
  [csv]
    type = CSV
  []
  exodus = false
[]

(modules/porous_flow/test/tests/gravity/grav02a.i)

# Checking that gravity head is established in the transient situation when 0<saturation<1 (note the strictly less-than).
# 2phase (PP), 2components, vanGenuchten, constant fluid bulk-moduli for each phase, constant viscosity, constant permeability, Corey relative perm
# For better agreement with the analytical solution (ana_pp), just increase nx

[Mesh]
  type = GeneratedMesh
  dim = 1
  nx = 10
  xmin = -1
  xmax = 0
[]

[GlobalParams]
  PorousFlowDictator = dictator
[]

[Variables]
  [ppwater]
    initial_condition = -1.0
  []
  [ppgas]
    initial_condition = 0
  []
[]

[AuxVariables]
  [massfrac_ph0_sp0]
    initial_condition = 1
  []
  [massfrac_ph1_sp0]
    initial_condition = 0
  []
[]


[Kernels]
  [mass0]
    type = PorousFlowMassTimeDerivative
    fluid_component = 0
    variable = ppwater
  []
  [flux0]
    type = PorousFlowAdvectiveFlux
    fluid_component = 0
    variable = ppwater
    gravity = '-1 0 0'
  []
  [mass1]
    type = PorousFlowMassTimeDerivative
    fluid_component = 1
    variable = ppgas
  []
  [flux1]
    type = PorousFlowAdvectiveFlux
    fluid_component = 1
    variable = ppgas
    gravity = '-1 0 0'
  []
[]


[Functions]
  [ana_ppwater]
    type = ParsedFunction
    symbol_names = 'g B p0 rho0'
    symbol_values = '1 2 pp_water_top 1'
    expression = '-B*log(exp(-p0/B)+g*rho0*x/B)' # expected pp at base
  []
  [ana_ppgas]
    type = ParsedFunction
    symbol_names = 'g B p0 rho0'
    symbol_values = '1 1 pp_gas_top 0.1'
    expression = '-B*log(exp(-p0/B)+g*rho0*x/B)' # expected pp at base
  []
[]

[UserObjects]
  [dictator]
    type = PorousFlowDictator
    porous_flow_vars = 'ppwater ppgas'
    number_fluid_phases = 2
    number_fluid_components = 2
  []
  [pc]
    type = PorousFlowCapillaryPressureVG
    m = 0.5
    alpha = 1
  []
[]

[FluidProperties]
  [simple_fluid0]
    type = SimpleFluidProperties
    bulk_modulus = 2
    density0 = 1
    viscosity = 1
    thermal_expansion = 0
  []
  [simple_fluid1]
    type = SimpleFluidProperties
    bulk_modulus = 1
    density0 = 0.1
    viscosity = 0.5
    thermal_expansion = 0
  []
[]

[Materials]
  [temperature]
    type = PorousFlowTemperature
  []
  [ppss]
    type = PorousFlow2PhasePP
    phase0_porepressure = ppwater
    phase1_porepressure = ppgas
    capillary_pressure = pc
  []
  [massfrac]
    type = PorousFlowMassFraction
    mass_fraction_vars = 'massfrac_ph0_sp0 massfrac_ph1_sp0'
  []
  [simple_fluid0]
    type = PorousFlowSingleComponentFluid
    fp = simple_fluid0
    phase = 0
  []
  [simple_fluid1]
    type = PorousFlowSingleComponentFluid
    fp = simple_fluid1
    phase = 1
  []
  [porosity]
    type = PorousFlowPorosityConst
    porosity = 0.1
  []
  [permeability]
    type = PorousFlowPermeabilityConst
    permeability = '1 0 0  0 2 0  0 0 3'
  []
  [relperm_water]
    type = PorousFlowRelativePermeabilityCorey
    n = 1
    phase = 0
  []
  [relperm_gas]
    type = PorousFlowRelativePermeabilityCorey
    n = 1
    phase = 1
  []
[]

[Postprocessors]
  [pp_water_top]
    type = PointValue
    variable = ppwater
    point = '0 0 0'
  []
  [pp_water_base]
    type = PointValue
    variable = ppwater
    point = '-1 0 0'
  []
  [pp_water_analytical]
    type = FunctionValuePostprocessor
    function = ana_ppwater
    point = '-1 0 0'
  []
  [pp_gas_top]
    type = PointValue
    variable = ppgas
    point = '0 0 0'
  []
  [pp_gas_base]
    type = PointValue
    variable = ppgas
    point = '-1 0 0'
  []
  [pp_gas_analytical]
    type = FunctionValuePostprocessor
    function = ana_ppgas
    point = '-1 0 0'
  []
  [mass_ph0]
    type = PorousFlowFluidMass
    fluid_component = 0
    execute_on = 'initial timestep_end'
  []
  [mass_ph1]
    type = PorousFlowFluidMass
    fluid_component = 1
    execute_on = 'initial timestep_end'
  []
[]

[Preconditioning]
  [andy]
    type = SMP
    full = true
  []
[]

[Executioner]
  type = Transient
  solve_type = Newton
  dt = 0.1
  end_time = 1.0
  nl_rel_tol = 1E-10
  nl_abs_tol = 1E-12
[]

[Outputs]
  [csv]
    type = CSV
    file_base = grav02a
    execute_on = 'initial final'
  []
[]

(modules/porous_flow/test/tests/gravity/grav02c.i)

# Checking that gravity head is established in the transient situation when 0<=saturation<=1 (note the less-than-or-equal-to).
# 2phase (PP), 2components, vanGenuchten, constant fluid bulk-moduli for each phase, constant viscosity, constant permeability, Corey relative perm
# For better agreement with the analytical solution (ana_pp), just increase nx

[Mesh]
  type = GeneratedMesh
  dim = 1
  nx = 10
  xmin = -1
  xmax = 0
[]

[GlobalParams]
  PorousFlowDictator = dictator
[]

[Functions]
  [dts]
    type = PiecewiseLinear
    y = '1E-3 1E-2 1E-1'
    x = '1E-3 1E-2 1E-1'
  []
[]

[Variables]
  [ppwater]
    initial_condition = -0.1
  []
  [ppgas]
    initial_condition = 0
  []
[]

[AuxVariables]
  [massfrac_ph0_sp0]
    initial_condition = 1
  []
  [massfrac_ph1_sp0]
    initial_condition = 0
  []
[]

[Kernels]
  [mass0]
    type = PorousFlowMassTimeDerivative
    fluid_component = 0
    variable = ppwater
  []
  [flux0]
    type = PorousFlowAdvectiveFlux
    fluid_component = 0
    variable = ppwater
    gravity = '-1 0 0'
  []
  [mass1]
    type = PorousFlowMassTimeDerivative
    fluid_component = 1
    variable = ppgas
  []
  [flux1]
    type = PorousFlowAdvectiveFlux
    fluid_component = 1
    variable = ppgas
    gravity = '-1 0 0'
  []
[]

[Functions]
  [ana_ppwater]
    type = ParsedFunction
    symbol_names = 'g B p0 rho0'
    symbol_values = '1 2 pp_water_top 1'
    expression = '-B*log(exp(-p0/B)+g*rho0*x/B)' # expected pp at base
  []
[]

[UserObjects]
  [dictator]
    type = PorousFlowDictator
    porous_flow_vars = 'ppwater ppgas'
    number_fluid_phases = 2
    number_fluid_components = 2
  []
  [pc]
    type = PorousFlowCapillaryPressureVG
    m = 0.5
    alpha = 1
  []
[]

[FluidProperties]
  [simple_fluid0]
    type = SimpleFluidProperties
    bulk_modulus = 2
    density0 = 1
    viscosity = 1
    thermal_expansion = 0
  []
  [simple_fluid1]
    type = SimpleFluidProperties
    bulk_modulus = 1
    density0 = 0.1
    viscosity = 0.5
    thermal_expansion = 0
  []
[]

[Materials]
  [temperature]
    type = PorousFlowTemperature
  []
  [ppss]
    type = PorousFlow2PhasePP
    phase0_porepressure = ppwater
    phase1_porepressure = ppgas
    capillary_pressure = pc
  []
  [massfrac]
    type = PorousFlowMassFraction
    mass_fraction_vars = 'massfrac_ph0_sp0 massfrac_ph1_sp0'
  []
  [simple_fluid0]
    type = PorousFlowSingleComponentFluid
    fp = simple_fluid0
    phase = 0
  []
  [simple_fluid1]
    type = PorousFlowSingleComponentFluid
    fp = simple_fluid1
    phase = 1
  []
  [porosity]
    type = PorousFlowPorosityConst
    porosity = 0.1
  []
  [permeability]
    type = PorousFlowPermeabilityConst
    permeability = '1 0 0  0 2 0  0 0 3'
  []
  [relperm_water]
    type = PorousFlowRelativePermeabilityCorey
    n = 1
    phase = 0
  []
  [relperm_gas]
    type = PorousFlowRelativePermeabilityCorey
    n = 1
    phase = 1
  []
[]

[Postprocessors]
  [pp_water_top]
    type = PointValue
    variable = ppwater
    point = '0 0 0'
  []
  [pp_water_base]
    type = PointValue
    variable = ppwater
    point = '-1 0 0'
  []
  [pp_water_analytical]
    type = FunctionValuePostprocessor
    function = ana_ppwater
    point = '-1 0 0'
  []
  [mass_ph0]
    type = PorousFlowFluidMass
    fluid_component = 0
    execute_on = 'initial timestep_end'
  []
  [mass_ph1]
    type = PorousFlowFluidMass
    fluid_component = 1
    execute_on = 'initial timestep_end'
  []

[]

[Preconditioning]
  active = andy
  [andy]
    type = SMP
    full = true
    petsc_options_iname = '-ksp_type -pc_type -snes_atol -snes_rtol -snes_max_it'
    petsc_options_value = 'bcgs bjacobi 1E-12 1E-10 10000'
  []
  [check]
    type = SMP
    full = true
    petsc_options_iname = '-ksp_type -pc_type -snes_atol -snes_rtol -snes_max_it -snes_type'
    petsc_options_value = 'bcgs bjacobi 1E-12 1E-10 10000 test'
  []
[]


[Executioner]
  type = Transient
  solve_type = Newton
  [TimeStepper]
    type = FunctionDT
    function = dts
  []
  end_time = 1.0
[]

[Outputs]
  execute_on = 'initial timestep_end'
  file_base = grav02c
  [csv]
    type = CSV
  []
  exodus = true
[]

(modules/porous_flow/test/tests/gravity/grav02d.i)

# Checking that gravity head is established in the transient situation when 0<=saturation<=1 (note the less-than-or-equal-to).
# 2phase (PP), 2components, vanGenuchten, constant fluid bulk-moduli for each phase, constant viscosity, constant permeability, Corey relative perm.
# A boundary condition enforces porepressures at the right boundary
# For better agreement with the analytical solution (ana_pp), just increase nx

[Mesh]
  type = GeneratedMesh
  dim = 1
  nx = 10
  xmin = -1
  xmax = 0
[]

[GlobalParams]
  PorousFlowDictator = dictator
[]

[Functions]
  [dts]
    type = PiecewiseLinear
    x = '1E-3 1E-2 1E-1 2E-1'
    y = '1E-3 1E-2 0.2E-1 1E-1'
  []
[]

[Variables]
  [ppwater]
    initial_condition = 0
  []
  [ppgas]
    initial_condition = 0.5
  []
[]

[AuxVariables]
  [massfrac_ph0_sp0]
    initial_condition = 1
  []
  [massfrac_ph1_sp0]
    initial_condition = 0
  []
[]

[BCs]
  [ppwater]
    type = DirichletBC
    boundary = right
    variable = ppwater
    value = 0
  []
  [ppgas]
    type = DirichletBC
    boundary = right
    variable = ppgas
    value = 0.5
  []
[]

[Kernels]
  [mass0]
    type = PorousFlowMassTimeDerivative
    fluid_component = 0
    variable = ppwater
  []
  [flux0]
    type = PorousFlowAdvectiveFlux
    fluid_component = 0
    variable = ppwater
    gravity = '-1 0 0'
  []
  [mass1]
    type = PorousFlowMassTimeDerivative
    fluid_component = 1
    variable = ppgas
  []
  [flux1]
    type = PorousFlowAdvectiveFlux
    fluid_component = 1
    variable = ppgas
    gravity = '-1 0 0'
  []
[]

[Functions]
  [ana_ppwater]
    type = ParsedFunction
    symbol_names = 'g B p0 rho0'
    symbol_values = '1 2 pp_water_top 1'
    expression = '-B*log(exp(-p0/B)+g*rho0*x/B)' # expected pp at base
  []
[]

[UserObjects]
  [dictator]
    type = PorousFlowDictator
    porous_flow_vars = 'ppwater ppgas'
    number_fluid_phases = 2
    number_fluid_components = 2
  []
  [pc]
    type = PorousFlowCapillaryPressureVG
    m = 0.5
    alpha = 1
  []
[]

[FluidProperties]
  [simple_fluid0]
    type = SimpleFluidProperties
    bulk_modulus = 1.2
    density0 = 1
    viscosity = 1
    thermal_expansion = 0
  []
  [simple_fluid1]
    type = SimpleFluidProperties
    bulk_modulus = 1
    density0 = 0.1
    viscosity = 0.5
    thermal_expansion = 0
  []
[]

[Materials]
  [temperature]
    type = PorousFlowTemperature
  []
  [ppss]
    type = PorousFlow2PhasePP
    phase0_porepressure = ppwater
    phase1_porepressure = ppgas
    capillary_pressure = pc
  []
  [massfrac]
    type = PorousFlowMassFraction
    mass_fraction_vars = 'massfrac_ph0_sp0 massfrac_ph1_sp0'
  []
  [simple_fluid0]
    type = PorousFlowSingleComponentFluid
    fp = simple_fluid0
    phase = 0
  []
  [simple_fluid1]
    type = PorousFlowSingleComponentFluid
    fp = simple_fluid1
    phase = 1
  []
  [porosity]
    type = PorousFlowPorosityConst
    porosity = 0.1
  []
  [permeability]
    type = PorousFlowPermeabilityConst
    permeability = '1 0 0  0 2 0  0 0 3'
  []
  [relperm_water]
    type = PorousFlowRelativePermeabilityCorey
    n = 1
    phase = 0
  []
  [relperm_gas]
    type = PorousFlowRelativePermeabilityCorey
    n = 1
    phase = 1
  []
[]

[Postprocessors]
  [pp_water_top]
    type = PointValue
    variable = ppwater
    point = '0 0 0'
  []
  [pp_water_base]
    type = PointValue
    variable = ppwater
    point = '-1 0 0'
  []
  [pp_water_analytical]
    type = FunctionValuePostprocessor
    function = ana_ppwater
    point = '-1 0 0'
  []
  [ppwater_00]
    type = PointValue
    variable = ppwater
    point = '0 0 0'
  []
  [ppwater_01]
    type = PointValue
    variable = ppwater
    point = '-0.1 0 0'
  []
  [ppwater_02]
    type = PointValue
    variable = ppwater
    point = '-0.2 0 0'
  []
  [ppwater_03]
    type = PointValue
    variable = ppwater
    point = '-0.3 0 0'
  []
  [ppwater_04]
    type = PointValue
    variable = ppwater
    point = '-0.4 0 0'
  []
  [ppwater_05]
    type = PointValue
    variable = ppwater
    point = '-0.5 0 0'
  []
  [ppwater_06]
    type = PointValue
    variable = ppwater
    point = '-0.6 0 0'
  []
  [ppwater_07]
    type = PointValue
    variable = ppwater
    point = '-0.7 0 0'
  []
  [ppwater_08]
    type = PointValue
    variable = ppwater
    point = '-0.8 0 0'
  []
  [ppwater_09]
    type = PointValue
    variable = ppwater
    point = '-0.9 0 0'
  []
  [ppwater_10]
    type = PointValue
    variable = ppwater
    point = '-1 0 0'
  []
  [ppgas_00]
    type = PointValue
    variable = ppgas
    point = '0 0 0'
  []
  [ppgas_01]
    type = PointValue
    variable = ppgas
    point = '-0.1 0 0'
  []
  [ppgas_02]
    type = PointValue
    variable = ppgas
    point = '-0.2 0 0'
  []
  [ppgas_03]
    type = PointValue
    variable = ppgas
    point = '-0.3 0 0'
  []
  [ppgas_04]
    type = PointValue
    variable = ppgas
    point = '-0.4 0 0'
  []
  [ppgas_05]
    type = PointValue
    variable = ppgas
    point = '-0.5 0 0'
  []
  [ppgas_06]
    type = PointValue
    variable = ppgas
    point = '-0.6 0 0'
  []
  [ppgas_07]
    type = PointValue
    variable = ppgas
    point = '-0.7 0 0'
  []
  [ppgas_08]
    type = PointValue
    variable = ppgas
    point = '-0.8 0 0'
  []
  [ppgas_09]
    type = PointValue
    variable = ppgas
    point = '-0.9 0 0'
  []
  [ppgas_10]
    type = PointValue
    variable = ppgas
    point = '-1 0 0'
  []
[]

[Preconditioning]
  active = andy
  [andy]
    type = SMP
    full = true
    petsc_options_iname = '-ksp_type -pc_type -snes_atol -snes_rtol -snes_max_it'
    petsc_options_value = 'bcgs bjacobi 1E-12 1E-10 10000'
  []
  [check]
    type = SMP
    full = true
    petsc_options_iname = '-ksp_type -pc_type -snes_atol -snes_rtol -snes_max_it -snes_type'
    petsc_options_value = 'bcgs bjacobi 1E-12 1E-10 10000 test'
  []
[]

[Executioner]
  type = Transient
  solve_type = Newton
  [TimeStepper]
    type = FunctionDT
    function = dts
  []
  end_time = 1.0
[]

[Outputs]
  [csv]
    type = CSV
    execute_on = 'initial final'
    file_base = grav02d
  []
[]

(modules/porous_flow/test/tests/gravity/grav02e.i)

# Checking that gravity head is established in the transient situation when 0<=saturation<=1 (note the less-than-or-equal-to).
# 2phase (PS), 2components, constant capillary pressure, constant fluid bulk-moduli for each phase, constant viscosity,
# constant permeability, Corey relative permeabilities with no residual saturation

[Mesh]
  type = GeneratedMesh
  dim = 2
  ny = 10
  ymax = 100
[]

[GlobalParams]
  PorousFlowDictator = dictator
  gravity = '0 -10 0'
[]

[Variables]
  [ppwater]
    initial_condition = 1.5e6
  []
  [sgas]
    initial_condition = 0.3
  []
[]

[AuxVariables]
  [massfrac_ph0_sp0]
    initial_condition = 1
  []
  [massfrac_ph1_sp0]
    initial_condition = 0
  []
  [ppgas]
    family = MONOMIAL
    order = FIRST
  []
  [swater]
    family = MONOMIAL
    order = FIRST
  []
  [relpermwater]
    family = MONOMIAL
    order = FIRST
  []
  [relpermgas]
    family = MONOMIAL
    order = FIRST
  []
[]

[Kernels]
  [mass0]
    type = PorousFlowMassTimeDerivative
    fluid_component = 0
    variable = ppwater
  []
  [flux0]
    type = PorousFlowAdvectiveFlux
    fluid_component = 0
    variable = ppwater
  []
  [mass1]
    type = PorousFlowMassTimeDerivative
    fluid_component = 1
    variable = sgas
  []
  [flux1]
    type = PorousFlowAdvectiveFlux
    fluid_component = 1
    variable = sgas
  []
[]

[AuxKernels]
  [ppgas]
    type = PorousFlowPropertyAux
    property = pressure
    phase = 1
    variable = ppgas
  []
  [swater]
    type = PorousFlowPropertyAux
    property = saturation
    phase = 0
    variable = swater
  []
  [relpermwater]
    type = PorousFlowPropertyAux
    property = relperm
    phase = 0
    variable = relpermwater
  []
  [relpermgas]
    type = PorousFlowPropertyAux
    property = relperm
    phase = 1
    variable = relpermgas
  []
[]

[UserObjects]
  [dictator]
    type = PorousFlowDictator
    porous_flow_vars = 'ppwater sgas'
    number_fluid_phases = 2
    number_fluid_components = 2
  []
  [pc]
    type = PorousFlowCapillaryPressureConst
    pc = 1e5
  []
[]

[FluidProperties]
  [simple_fluid0]
    type = SimpleFluidProperties
    bulk_modulus = 2e9
    density0 = 1000
    viscosity = 1e-3
    thermal_expansion = 0
  []
  [simple_fluid1]
    type = SimpleFluidProperties
    bulk_modulus = 2e9
    density0 = 10
    viscosity = 1e-5
    thermal_expansion = 0
  []
[]

[Materials]
  [temperature]
    type = PorousFlowTemperature
  []
  [ppss]
    type = PorousFlow2PhasePS
    phase0_porepressure = ppwater
    phase1_saturation = sgas
    capillary_pressure = pc
  []
  [massfrac]
    type = PorousFlowMassFraction
    mass_fraction_vars = 'massfrac_ph0_sp0 massfrac_ph1_sp0'
  []
  [simple_fluid0]
    type = PorousFlowSingleComponentFluid
    fp = simple_fluid0
    phase = 0
  []
  [simple_fluid1]
    type = PorousFlowSingleComponentFluid
    fp = simple_fluid1
    phase = 1
  []
  [porosity]
    type = PorousFlowPorosityConst
    porosity = 0.1
  []
  [permeability]
    type = PorousFlowPermeabilityConst
    permeability = '1e-11 0 0 0 1e-11 0  0 0 1e-11'
  []
  [relperm_water]
    type = PorousFlowRelativePermeabilityCorey
    n = 2
    phase = 0
  []
  [relperm_gas]
    type = PorousFlowRelativePermeabilityCorey
    n = 2
    phase = 1
  []
[]

[Postprocessors]
  [mass_ph0]
    type = PorousFlowFluidMass
    fluid_component = 0
    execute_on = 'initial timestep_end'
  []
  [mass_ph1]
    type = PorousFlowFluidMass
    fluid_component = 1
    execute_on = 'initial timestep_end'
  []
[]

[Preconditioning]
  [smp]
    type = SMP
    full = true
    petsc_options_iname = '-ksp_type -pc_type -snes_atol -snes_rtol'
    petsc_options_value = 'bcgs bjacobi 1E-12 1E-10'
  []
[]

[Executioner]
  type = Transient
  solve_type = Newton
  end_time = 1e5
  [TimeStepper]
    type = IterationAdaptiveDT
    dt = 1e4
  []
[]

[Outputs]
  execute_on = 'initial timestep_end'
  file_base = grav02e
  exodus = true
  perf_graph = true
  csv = false
[]

(modules/porous_flow/test/tests/gravity/grav02f.i)

# Checking that gravity head is established in the transient situation when 0<=saturation<=1 (note the less-than-or-equal-to).
# 2phase (PS), 2components, van Genuchten capillary pressure, constant fluid bulk-moduli for each phase, constant viscosity,
# constant permeability, Corey relative permeabilities with residual saturation

[Mesh]
  type = GeneratedMesh
  dim = 2
  ny = 10
  ymax = 100
[]

[GlobalParams]
  PorousFlowDictator = dictator
  gravity = '0 -10 0'
[]

[Variables]
  [ppwater]
    initial_condition = 1.5e6
  []
  [sgas]
    initial_condition = 0.3
  []
[]

[AuxVariables]
  [massfrac_ph0_sp0]
    initial_condition = 1
  []
  [massfrac_ph1_sp0]
    initial_condition = 0
  []
  [ppgas]
    family = MONOMIAL
    order = CONSTANT
  []
  [swater]
    family = MONOMIAL
    order = CONSTANT
  []
  [relpermwater]
    family = MONOMIAL
    order = CONSTANT
  []
  [relpermgas]
    family = MONOMIAL
    order = CONSTANT
  []
[]

[Kernels]
  [mass0]
    type = PorousFlowMassTimeDerivative
    fluid_component = 0
    variable = ppwater
  []
  [flux0]
    type = PorousFlowAdvectiveFlux
    fluid_component = 0
    variable = ppwater
  []
  [mass1]
    type = PorousFlowMassTimeDerivative
    fluid_component = 1
    variable = sgas
  []
  [flux1]
    type = PorousFlowAdvectiveFlux
    fluid_component = 1
    variable = sgas
  []
[]

[AuxKernels]
  [ppgas]
    type = PorousFlowPropertyAux
    property = pressure
    phase = 1
    variable = ppgas
  []
  [swater]
    type = PorousFlowPropertyAux
    property = saturation
    phase = 0
    variable = swater
  []
  [relpermwater]
    type = MaterialStdVectorAux
    property = PorousFlow_relative_permeability_qp
    index = 0
    variable = relpermwater
  []
  [relpermgas]
    type = PorousFlowPropertyAux
    property = relperm
    phase = 1
    variable = relpermgas
  []
[]

[UserObjects]
  [dictator]
    type = PorousFlowDictator
    porous_flow_vars = 'ppwater sgas'
    number_fluid_phases = 2
    number_fluid_components = 2
  []
  [pc]
    type = PorousFlowCapillaryPressureVG
    m = 0.5
    alpha = 1e-4
    pc_max = 2e5
  []
[]

[FluidProperties]
  [simple_fluid0]
    type = SimpleFluidProperties
    bulk_modulus = 2e9
    density0 = 1000
    viscosity = 1e-3
    thermal_expansion = 0
  []
  [simple_fluid1]
    type = SimpleFluidProperties
    bulk_modulus = 2e9
    density0 = 10
    viscosity = 1e-5
    thermal_expansion = 0
  []
[]

[Materials]
  [temperature]
    type = PorousFlowTemperature
  []
  [ppss]
    type = PorousFlow2PhasePS
    phase0_porepressure = ppwater
    phase1_saturation = sgas
    capillary_pressure = pc
  []
  [massfrac]
    type = PorousFlowMassFraction
    mass_fraction_vars = 'massfrac_ph0_sp0 massfrac_ph1_sp0'
  []
  [simple_fluid0]
    type = PorousFlowSingleComponentFluid
    fp = simple_fluid0
    phase = 0
  []
  [simple_fluid1]
    type = PorousFlowSingleComponentFluid
    fp = simple_fluid1
    phase = 1
  []
  [porosity]
    type = PorousFlowPorosityConst
    porosity = 0.1
  []
  [permeability]
    type = PorousFlowPermeabilityConst
    permeability = '1e-11 0 0 0 1e-11 0  0 0 1e-11'
  []
  [relperm_water]
    type = PorousFlowRelativePermeabilityCorey
    n = 2
    phase = 0
    s_res = 0.25
    sum_s_res = 0.35
  []
  [relperm_gas]
    type = PorousFlowRelativePermeabilityCorey
    n = 2
    phase = 1
    s_res = 0.1
    sum_s_res = 0.35
  []
[]

[Postprocessors]
  [mass_ph0]
    type = PorousFlowFluidMass
    fluid_component = 0
    execute_on = 'initial timestep_end'
  []
  [mass_ph1]
    type = PorousFlowFluidMass
    fluid_component = 1
    execute_on = 'initial timestep_end'
  []
[]

[Preconditioning]
  [smp]
    type = SMP
    full = true
    petsc_options_iname = '-ksp_type -pc_type -snes_stol -snes_max_it'
    petsc_options_value = 'bcgs bjacobi 1E-13 15'
  []
[]

[Executioner]
  type = Transient
  solve_type = Newton
  end_time = 1e5
  [TimeStepper]
    type = IterationAdaptiveDT
    dt = 1e4
  []
[]

[Outputs]
  execute_on = 'initial timestep_end'
  file_base = grav02f
  exodus = true
  perf_graph = true
  csv = false
[]

(modules/porous_flow/test/tests/gravity/grav02f.i)

# Checking that gravity head is established in the transient situation when 0<=saturation<=1 (note the less-than-or-equal-to).
# 2phase (PS), 2components, van Genuchten capillary pressure, constant fluid bulk-moduli for each phase, constant viscosity,
# constant permeability, Corey relative permeabilities with residual saturation

[Mesh]
  type = GeneratedMesh
  dim = 2
  ny = 10
  ymax = 100
[]

[GlobalParams]
  PorousFlowDictator = dictator
  gravity = '0 -10 0'
[]

[Variables]
  [ppwater]
    initial_condition = 1.5e6
  []
  [sgas]
    initial_condition = 0.3
  []
[]

[AuxVariables]
  [massfrac_ph0_sp0]
    initial_condition = 1
  []
  [massfrac_ph1_sp0]
    initial_condition = 0
  []
  [ppgas]
    family = MONOMIAL
    order = CONSTANT
  []
  [swater]
    family = MONOMIAL
    order = CONSTANT
  []
  [relpermwater]
    family = MONOMIAL
    order = CONSTANT
  []
  [relpermgas]
    family = MONOMIAL
    order = CONSTANT
  []
[]

[Kernels]
  [mass0]
    type = PorousFlowMassTimeDerivative
    fluid_component = 0
    variable = ppwater
  []
  [flux0]
    type = PorousFlowAdvectiveFlux
    fluid_component = 0
    variable = ppwater
  []
  [mass1]
    type = PorousFlowMassTimeDerivative
    fluid_component = 1
    variable = sgas
  []
  [flux1]
    type = PorousFlowAdvectiveFlux
    fluid_component = 1
    variable = sgas
  []
[]

[AuxKernels]
  [ppgas]
    type = PorousFlowPropertyAux
    property = pressure
    phase = 1
    variable = ppgas
  []
  [swater]
    type = PorousFlowPropertyAux
    property = saturation
    phase = 0
    variable = swater
  []
  [relpermwater]
    type = MaterialStdVectorAux
    property = PorousFlow_relative_permeability_qp
    index = 0
    variable = relpermwater
  []
  [relpermgas]
    type = PorousFlowPropertyAux
    property = relperm
    phase = 1
    variable = relpermgas
  []
[]

[UserObjects]
  [dictator]
    type = PorousFlowDictator
    porous_flow_vars = 'ppwater sgas'
    number_fluid_phases = 2
    number_fluid_components = 2
  []
  [pc]
    type = PorousFlowCapillaryPressureVG
    m = 0.5
    alpha = 1e-4
    pc_max = 2e5
  []
[]

[FluidProperties]
  [simple_fluid0]
    type = SimpleFluidProperties
    bulk_modulus = 2e9
    density0 = 1000
    viscosity = 1e-3
    thermal_expansion = 0
  []
  [simple_fluid1]
    type = SimpleFluidProperties
    bulk_modulus = 2e9
    density0 = 10
    viscosity = 1e-5
    thermal_expansion = 0
  []
[]

[Materials]
  [temperature]
    type = PorousFlowTemperature
  []
  [ppss]
    type = PorousFlow2PhasePS
    phase0_porepressure = ppwater
    phase1_saturation = sgas
    capillary_pressure = pc
  []
  [massfrac]
    type = PorousFlowMassFraction
    mass_fraction_vars = 'massfrac_ph0_sp0 massfrac_ph1_sp0'
  []
  [simple_fluid0]
    type = PorousFlowSingleComponentFluid
    fp = simple_fluid0
    phase = 0
  []
  [simple_fluid1]
    type = PorousFlowSingleComponentFluid
    fp = simple_fluid1
    phase = 1
  []
  [porosity]
    type = PorousFlowPorosityConst
    porosity = 0.1
  []
  [permeability]
    type = PorousFlowPermeabilityConst
    permeability = '1e-11 0 0 0 1e-11 0  0 0 1e-11'
  []
  [relperm_water]
    type = PorousFlowRelativePermeabilityCorey
    n = 2
    phase = 0
    s_res = 0.25
    sum_s_res = 0.35
  []
  [relperm_gas]
    type = PorousFlowRelativePermeabilityCorey
    n = 2
    phase = 1
    s_res = 0.1
    sum_s_res = 0.35
  []
[]

[Postprocessors]
  [mass_ph0]
    type = PorousFlowFluidMass
    fluid_component = 0
    execute_on = 'initial timestep_end'
  []
  [mass_ph1]
    type = PorousFlowFluidMass
    fluid_component = 1
    execute_on = 'initial timestep_end'
  []
[]

[Preconditioning]
  [smp]
    type = SMP
    full = true
    petsc_options_iname = '-ksp_type -pc_type -snes_stol -snes_max_it'
    petsc_options_value = 'bcgs bjacobi 1E-13 15'
  []
[]

[Executioner]
  type = Transient
  solve_type = Newton
  end_time = 1e5
  [TimeStepper]
    type = IterationAdaptiveDT
    dt = 1e4
  []
[]

[Outputs]
  execute_on = 'initial timestep_end'
  file_base = grav02f
  exodus = true
  perf_graph = true
  csv = false
[]

Single - phase , single - component
Two - phase , two - component