Pressure-pulses in 1D

The PorousFlow fluid equation for single-phase flow through a fully saturated medium without gravity and without sources is just Darcy's equation $var element = document.getElementById("moose-equation-a73e5a32-ed65-4e58-8143-d218635f1d7a");katex.render("\\frac{\\partial}{\\partial t}\\phi\\rho = \\nabla_{i}\\left(\\frac{\\rho \\kappa_{ij}}{\\mu} \\nabla_{j}P \\right) \\ ,", element, {displayMode:true,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ with notation described in the governing equations. Using $var element = document.getElementById("moose-equation-2a2c3b6c-0bd0-4dd6-8fc6-a2759f190891");katex.render("\\rho \\propto \\exp(P/K)", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ , where $var element = document.getElementById("moose-equation-1c43da7f-901f-4eb2-87fa-691e9de0d3ea");katex.render("K", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ is the fluid bulk modulus, Darcy's equation becomes $var element = document.getElementById("moose-equation-e48c0cfa-9244-46df-a0d0-e22f1bdb1b41");katex.render("\\frac{\\partial}{\\partial t}\\rho = \\nabla_{i}\\alpha_{ij}\\nabla\\rho \\ ,", element, {displayMode:true,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ with $var element = document.getElementById("moose-equation-df3720cd-6f43-4f3d-b5cb-771f04315908");katex.render("\\alpha_{ij} = \\frac{\\kappa_{ij}B}{\\mu\\phi} \\ .", element, {displayMode:true,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ Here I've assumed the porosity and bulk modulus are constant in space and time.

Consider the one-dimensional case were the spatial dimension is the semi-infinite line $var element = document.getElementById("moose-equation-726af44f-4586-4585-b7f1-fd73612af26b");katex.render("x\\geq 0", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ . Suppose that initially the pressure is constant, so that $var element = document.getElementById("moose-equation-d9023921-f2e8-4d18-a10b-bbbfb750f8b2");katex.render("\\rho(x, t=0) = \\rho_{0} \\ \\ \\ \\mathrm{for }\\ \\ x\\geq 0 \\ .", element, {displayMode:true,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ Then apply a fixed-pressure Dirichlet boundary condition at $var element = document.getElementById("moose-equation-21101588-edcb-4f48-b821-56ea236f8ae4");katex.render("x=0", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ so that $var element = document.getElementById("moose-equation-027ca81b-707a-4100-8747-2fc00de580df");katex.render("\\rho(x=0, t>0) = \\rho_{\\infty}", element, {displayMode:true,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ The solution of the above differential equation is well known to be $(1)var element = document.getElementById("moose-equation-d8aa9505-5187-4dcb-a638-268746d0a270");katex.render("\\rho(x, t) = \\rho_{\\infty} + (\\rho_{0} - \\rho_{\\infty})\\,\\mathrm{Erf}\\left( \\frac{x}{\\sqrt{4\\alpha t}} \\right) \\ , ", element, {displayMode:true,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ where Erf is the error function.

A number of PorousFlow tests verify that this solution is produced with parameters shown in Table 1

Table 1: Parameter values used in the pressure-pulse tests

Parameter	Value
length of 1D bar	100 m
number of elements	10
end time (for transient simulations)	10000 s
number of time steps	10
Fluid bulk modulus ( $var element = document.getElementById("moose-equation-7e96b39f-a027-42f2-b3ef-051a684011ff");katex.render("B", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ )	2 GPa
Fluid viscosity ( $var element = document.getElementById("moose-equation-6e8b2087-23e7-4e09-bfd6-e76ddf55bd15");katex.render("\\mu", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ )	0.001 Pa.s
Permeability ( $var element = document.getElementById("moose-equation-afd05033-de06-41ed-b177-9da61d30b768");katex.render("\\kappa_{xx}", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ )	$var element = document.getElementById("moose-equation-8d9b45d8-ae02-41ee-bf6e-0956e6d290a7");katex.render("10^{-15}\\,", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ m $var element = document.getElementById("moose-equation-3cfd1fb6-79e6-4a08-b85c-4cf296db7faf");katex.render("^{2}", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$
Porosity	0.1
Initial pressure	2 MPa
Applied pressure	3 MPa

The tests include:

Steady state 1-phase analysis to demonstrate that the steady-state of $var element = document.getElementById("moose-equation-7716a676-8864-4b16-9a8b-3a06994fed7a");katex.render("\\rho = \\rho_{\\infty}", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ is achieved.

# Pressure pulse in 1D with 1 phase - steady
# This file employs the PorousFlowFullySaturated Action.  For the non-Action version see pressure_pulse_1d.i
[Mesh]
  type = GeneratedMesh
  dim = 1
  nx = 10
  xmin = 0
  xmax = 100
[]

[GlobalParams]
  PorousFlowDictator = dictator
[]

[Variables]
  [pp]
    initial_condition = 2E6
  []
[]

[PorousFlowFullySaturated]
  porepressure = pp
  gravity = '0 0 0'
  fp = simple_fluid
  stabilization = Full
[]

[Modules]
  [FluidProperties]
    [simple_fluid]
      type = SimpleFluidProperties
      bulk_modulus = 2e9
      density0 = 1000
      thermal_expansion = 0
      viscosity = 1e-3
    []
  []
[]

[Materials]
  [permeability]
    type = PorousFlowPermeabilityConst
    permeability = '1E-15 0 0 0 1E-15 0 0 0 1E-15'
  []
[]

[BCs]
  [left]
    type = DirichletBC
    boundary = left
    value = 3E6
    variable = pp
  []
[]

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

[Executioner]
  type = Steady
  solve_type = Newton
[]

[Postprocessors]
  [p000]
    type = PointValue
    variable = pp
    point = '0 0 0'
    execute_on = 'initial timestep_end'
  []
  [p010]
    type = PointValue
    variable = pp
    point = '10 0 0'
    execute_on = 'initial timestep_end'
  []
  [p020]
    type = PointValue
    variable = pp
    point = '20 0 0'
    execute_on = 'initial timestep_end'
  []
  [p030]
    type = PointValue
    variable = pp
    point = '30 0 0'
    execute_on = 'initial timestep_end'
  []
  [p040]
    type = PointValue
    variable = pp
    point = '40 0 0'
    execute_on = 'initial timestep_end'
  []
  [p050]
    type = PointValue
    variable = pp
    point = '50 0 0'
    execute_on = 'initial timestep_end'
  []
  [p060]
    type = PointValue
    variable = pp
    point = '60 0 0'
    execute_on = 'initial timestep_end'
  []
  [p070]
    type = PointValue
    variable = pp
    point = '70 0 0'
    execute_on = 'initial timestep_end'
  []
  [p080]
    type = PointValue
    variable = pp
    point = '80 0 0'
    execute_on = 'initial timestep_end'
  []
  [p090]
    type = PointValue
    variable = pp
    point = '90 0 0'
    execute_on = 'initial timestep_end'
  []
  [p100]
    type = PointValue
    variable = pp
    point = '100 0 0'
    execute_on = 'initial timestep_end'
  []
[]

[Outputs]
  file_base = pressure_pulse_1d_steady
  print_linear_residuals = false
  csv = true
[]

Transient 1-phase analysis.

# Pressure pulse in 1D with 1 phase - transient
# This input file uses the PorousFlowFullySaturated Action.  For the non-Action version, see pressure_pulse_1d.i
[Mesh]
  type = GeneratedMesh
  dim = 1
  nx = 10
  xmin = 0
  xmax = 100
[]

[GlobalParams]
  PorousFlowDictator = dictator
[]

[Variables]
  [pp]
    initial_condition = 2E6
  []
[]

[PorousFlowFullySaturated]
  porepressure = pp
  gravity = '0 0 0'
  fp = simple_fluid
  stabilization = Full
[]

[Modules]
  [FluidProperties]
    [simple_fluid]
      type = SimpleFluidProperties
      bulk_modulus = 2e9
      density0 = 1000
      thermal_expansion = 0
      viscosity = 1e-3
    []
  []
[]

[Materials]
  [porosity]
    type = PorousFlowPorosityConst
    porosity = 0.1
  []
  [permeability]
    type = PorousFlowPermeabilityConst
    permeability = '1E-15 0 0 0 1E-15 0 0 0 1E-15'
  []
[]

[BCs]
  [left]
    type = DirichletBC
    boundary = left
    value = 3E6
    variable = pp
  []
[]

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

[Executioner]
  type = Transient
  solve_type = Newton
  dt = 1E3
  end_time = 1E4
[]

[Postprocessors]
  [p000]
    type = PointValue
    variable = pp
    point = '0 0 0'
    execute_on = 'initial timestep_end'
  []
  [p010]
    type = PointValue
    variable = pp
    point = '10 0 0'
    execute_on = 'initial timestep_end'
  []
  [p020]
    type = PointValue
    variable = pp
    point = '20 0 0'
    execute_on = 'initial timestep_end'
  []
  [p030]
    type = PointValue
    variable = pp
    point = '30 0 0'
    execute_on = 'initial timestep_end'
  []
  [p040]
    type = PointValue
    variable = pp
    point = '40 0 0'
    execute_on = 'initial timestep_end'
  []
  [p050]
    type = PointValue
    variable = pp
    point = '50 0 0'
    execute_on = 'initial timestep_end'
  []
  [p060]
    type = PointValue
    variable = pp
    point = '60 0 0'
    execute_on = 'initial timestep_end'
  []
  [p070]
    type = PointValue
    variable = pp
    point = '70 0 0'
    execute_on = 'initial timestep_end'
  []
  [p080]
    type = PointValue
    variable = pp
    point = '80 0 0'
    execute_on = 'initial timestep_end'
  []
  [p090]
    type = PointValue
    variable = pp
    point = '90 0 0'
    execute_on = 'initial timestep_end'
  []
  [p100]
    type = PointValue
    variable = pp
    point = '100 0 0'
    execute_on = 'initial timestep_end'
  []
[]

[Outputs]
  file_base = pressure_pulse_1d
  print_linear_residuals = false
  csv = true
[]

Transient 1-phase, 3 component analysis to check that the components diffuse at the same rate.

# Pressure pulse in 1D with 1 phase but 3 components (viscosity, relperm, etc are independent of mass-fractions) - transient
# This input file uses the PorousFlowFullySaturated Action.  For the non-Action version, see pressure_pulse_1d_3comp.i
[Mesh]
  type = GeneratedMesh
  dim = 1
  nx = 10
  xmin = 0
  xmax = 100
[]

[GlobalParams]
  PorousFlowDictator = dictator
[]

[Variables]
  [pp]
    initial_condition = 2E6
  []
  [massfrac0]
    initial_condition = 0.1
  []
  [massfrac1]
    initial_condition = 0.3
  []
[]

[PorousFlowFullySaturated]
  porepressure = pp
  mass_fraction_vars = 'massfrac0 massfrac1'
  gravity = '0 0 0'
  fp = simple_fluid
  stabilization = Full
[]

[Modules]
  [FluidProperties]
    [simple_fluid]
      type = SimpleFluidProperties
      bulk_modulus = 2e9
      density0 = 1000
      thermal_expansion = 0
      viscosity = 1e-3
    []
  []
[]

[Materials]
  [porosity]
    type = PorousFlowPorosityConst
    porosity = 0.1
  []
  [permeability]
    type = PorousFlowPermeabilityConst
    permeability = '1E-15 0 0 0 1E-15 0 0 0 1E-15'
  []
[]

[BCs]
  [left]
    type = DirichletBC
    boundary = left
    value = 3E6
    variable = pp
  []
[]

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

[Executioner]
  type = Transient
  solve_type = Newton
  dt = 1E3
  end_time = 1E4
[]

[Postprocessors]
  [p000]
    type = PointValue
    variable = pp
    point = '0 0 0'
    execute_on = 'initial timestep_end'
  []
  [p010]
    type = PointValue
    variable = pp
    point = '10 0 0'
    execute_on = 'initial timestep_end'
  []
  [p020]
    type = PointValue
    variable = pp
    point = '20 0 0'
    execute_on = 'initial timestep_end'
  []
  [p030]
    type = PointValue
    variable = pp
    point = '30 0 0'
    execute_on = 'initial timestep_end'
  []
  [p040]
    type = PointValue
    variable = pp
    point = '40 0 0'
    execute_on = 'initial timestep_end'
  []
  [p050]
    type = PointValue
    variable = pp
    point = '50 0 0'
    execute_on = 'initial timestep_end'
  []
  [p060]
    type = PointValue
    variable = pp
    point = '60 0 0'
    execute_on = 'initial timestep_end'
  []
  [p070]
    type = PointValue
    variable = pp
    point = '70 0 0'
    execute_on = 'initial timestep_end'
  []
  [p080]
    type = PointValue
    variable = pp
    point = '80 0 0'
    execute_on = 'initial timestep_end'
  []
  [p090]
    type = PointValue
    variable = pp
    point = '90 0 0'
    execute_on = 'initial timestep_end'
  []
  [p100]
    type = PointValue
    variable = pp
    point = '100 0 0'
    execute_on = 'initial timestep_end'
  []
  [mf_0_010]
    type = PointValue
    variable = massfrac0
    point = '10 0 0'
    execute_on = 'timestep_end'
  []
  [mf_1_010]
    type = PointValue
    variable = massfrac1
    point = '10 0 0'
    execute_on = 'timestep_end'
  []
[]

[Outputs]
  file_base = pressure_pulse_1d_3comp
  print_linear_residuals = true
  csv = true
[]

Transient 2-phase analysis, with the "water" state fully saturated.

# Pressure pulse in 1D with 2 phases (with one having zero saturation), 2components - transient
[Mesh]
  type = GeneratedMesh
  dim = 1
  nx = 10
  xmin = 0
  xmax = 100
[]

[GlobalParams]
  PorousFlowDictator = dictator
[]

[Variables]
  [ppwater]
    initial_condition = 2E6
  []
  [ppgas]
    initial_condition = 2E6
  []
[]

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

[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
  []
[]

[Modules]
  [FluidProperties]
    [simple_fluid0]
      type = SimpleFluidProperties
      bulk_modulus = 2e9
      density0 = 1000
      thermal_expansion = 0
      viscosity = 1e-3
    []
    [simple_fluid1]
      type = SimpleFluidProperties
      bulk_modulus = 2e6
      density0 = 1
      thermal_expansion = 0
      viscosity = 1e-5
    []
  []
[]

[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 = '1E-15 0 0 0 1E-15 0 0 0 1E-15'
  []
  [relperm_water]
    type = PorousFlowRelativePermeabilityCorey
    n = 1
    phase = 0
  []
  [relperm_gas]
    type = PorousFlowRelativePermeabilityCorey
    n = 1
    phase = 1
  []
[]

[BCs]
  [leftwater]
    type = DirichletBC
    boundary = left
    value = 3E6
    variable = ppwater
  []
  [leftgas]
    type = DirichletBC
    boundary = left
    value = 3E6
    variable = ppgas
  []
[]

[Preconditioning]
  [andy]
    type = SMP
    full = true
    petsc_options = '-snes_converged_reason -ksp_diagonal_scale -ksp_diagonal_scale_fix -ksp_gmres_modifiedgramschmidt -snes_linesearch_monitor'
    petsc_options_iname = '-ksp_type -pc_type -sub_pc_type -sub_pc_factor_shift_type -pc_asm_overlap -snes_atol -snes_rtol -snes_max_it'
    petsc_options_value = 'gmres      asm      lu           NONZERO                   2               1E-15       1E-20 20'
  []
[]

[Executioner]
  type = Transient
  solve_type = Newton
  dt = 1E3
  end_time = 1E4
[]

[Postprocessors]
  [p000]
    type = PointValue
    variable = ppwater
    point = '0 0 0'
    execute_on = 'initial timestep_end'
  []
  [p010]
    type = PointValue
    variable = ppwater
    point = '10 0 0'
    execute_on = 'initial timestep_end'
  []
  [p020]
    type = PointValue
    variable = ppwater
    point = '20 0 0'
    execute_on = 'initial timestep_end'
  []
  [p030]
    type = PointValue
    variable = ppwater
    point = '30 0 0'
    execute_on = 'initial timestep_end'
  []
  [p040]
    type = PointValue
    variable = ppwater
    point = '40 0 0'
    execute_on = 'initial timestep_end'
  []
  [p050]
    type = PointValue
    variable = ppwater
    point = '50 0 0'
    execute_on = 'initial timestep_end'
  []
  [p060]
    type = PointValue
    variable = ppwater
    point = '60 0 0'
    execute_on = 'initial timestep_end'
  []
  [p070]
    type = PointValue
    variable = ppwater
    point = '70 0 0'
    execute_on = 'initial timestep_end'
  []
  [p080]
    type = PointValue
    variable = ppwater
    point = '80 0 0'
    execute_on = 'initial timestep_end'
  []
  [p090]
    type = PointValue
    variable = ppwater
    point = '90 0 0'
    execute_on = 'initial timestep_end'
  []
  [p100]
    type = PointValue
    variable = ppwater
    point = '100 0 0'
    execute_on = 'initial timestep_end'
  []
[]

[Outputs]
  file_base = pressure_pulse_1d_2phase
  print_linear_residuals = false
  csv = true
[]

Transient 2-phase using the "PS" formulation
2-phase using the "PS" formulation and Kuzmin-Turek stabilisation
2 phase using the PS formulation and a van Genuchten capillary pressure
2 phase using the PS formulation and a van Genuchten capillary pressure with a logarithmic extension;
1 phase when the primary variable is $var element = document.getElementById("moose-equation-dfe0188d-5605-4ee8-b64a-02ddb77a8ffa");katex.render("\\mathrm{log}\\,\\rho", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$
1 phase using the fully-saturated version of PorousFlow (no upwinding and no mass lumping)
1 phase with 3 fluid components using the fully-saturated version of PorousFlow (no upwinding and no mass lumping)

An example verification is shown in Figure 1.

Figure 1: Comparison between the MOOSE result (in dots), and the exact analytic expression given by Eq. (1). The agreement increases for greater spatial resolution and smaller timesteps. Both the multi-component single-phase simulation (using the fully-saturated non-upwinding Kernels, or the partially-saturated full-upwinding Kernels, or the log(mass-density) primary variable) and the 2-phase fully-water-saturated simulation give identical results for the water porepressure.

(modules/porous_flow/test/tests/pressure_pulse/pressure_pulse_1d_steady_action.i)

# Pressure pulse in 1D with 1 phase - steady
# This file employs the PorousFlowFullySaturated Action.  For the non-Action version see pressure_pulse_1d.i
[Mesh]
  type = GeneratedMesh
  dim = 1
  nx = 10
  xmin = 0
  xmax = 100
[]

[GlobalParams]
  PorousFlowDictator = dictator
[]

[Variables]
  [pp]
    initial_condition = 2E6
  []
[]

[PorousFlowFullySaturated]
  porepressure = pp
  gravity = '0 0 0'
  fp = simple_fluid
  stabilization = Full
[]

[Modules]
  [FluidProperties]
    [simple_fluid]
      type = SimpleFluidProperties
      bulk_modulus = 2e9
      density0 = 1000
      thermal_expansion = 0
      viscosity = 1e-3
    []
  []
[]

[Materials]
  [permeability]
    type = PorousFlowPermeabilityConst
    permeability = '1E-15 0 0 0 1E-15 0 0 0 1E-15'
  []
[]

[BCs]
  [left]
    type = DirichletBC
    boundary = left
    value = 3E6
    variable = pp
  []
[]

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

[Executioner]
  type = Steady
  solve_type = Newton
[]

[Postprocessors]
  [p000]
    type = PointValue
    variable = pp
    point = '0 0 0'
    execute_on = 'initial timestep_end'
  []
  [p010]
    type = PointValue
    variable = pp
    point = '10 0 0'
    execute_on = 'initial timestep_end'
  []
  [p020]
    type = PointValue
    variable = pp
    point = '20 0 0'
    execute_on = 'initial timestep_end'
  []
  [p030]
    type = PointValue
    variable = pp
    point = '30 0 0'
    execute_on = 'initial timestep_end'
  []
  [p040]
    type = PointValue
    variable = pp
    point = '40 0 0'
    execute_on = 'initial timestep_end'
  []
  [p050]
    type = PointValue
    variable = pp
    point = '50 0 0'
    execute_on = 'initial timestep_end'
  []
  [p060]
    type = PointValue
    variable = pp
    point = '60 0 0'
    execute_on = 'initial timestep_end'
  []
  [p070]
    type = PointValue
    variable = pp
    point = '70 0 0'
    execute_on = 'initial timestep_end'
  []
  [p080]
    type = PointValue
    variable = pp
    point = '80 0 0'
    execute_on = 'initial timestep_end'
  []
  [p090]
    type = PointValue
    variable = pp
    point = '90 0 0'
    execute_on = 'initial timestep_end'
  []
  [p100]
    type = PointValue
    variable = pp
    point = '100 0 0'
    execute_on = 'initial timestep_end'
  []
[]

[Outputs]
  file_base = pressure_pulse_1d_steady
  print_linear_residuals = false
  csv = true
[]

(modules/porous_flow/test/tests/pressure_pulse/pressure_pulse_1d_action.i)

# Pressure pulse in 1D with 1 phase - transient
# This input file uses the PorousFlowFullySaturated Action.  For the non-Action version, see pressure_pulse_1d.i
[Mesh]
  type = GeneratedMesh
  dim = 1
  nx = 10
  xmin = 0
  xmax = 100
[]

[GlobalParams]
  PorousFlowDictator = dictator
[]

[Variables]
  [pp]
    initial_condition = 2E6
  []
[]

[PorousFlowFullySaturated]
  porepressure = pp
  gravity = '0 0 0'
  fp = simple_fluid
  stabilization = Full
[]

[Modules]
  [FluidProperties]
    [simple_fluid]
      type = SimpleFluidProperties
      bulk_modulus = 2e9
      density0 = 1000
      thermal_expansion = 0
      viscosity = 1e-3
    []
  []
[]

[Materials]
  [porosity]
    type = PorousFlowPorosityConst
    porosity = 0.1
  []
  [permeability]
    type = PorousFlowPermeabilityConst
    permeability = '1E-15 0 0 0 1E-15 0 0 0 1E-15'
  []
[]

[BCs]
  [left]
    type = DirichletBC
    boundary = left
    value = 3E6
    variable = pp
  []
[]

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

[Executioner]
  type = Transient
  solve_type = Newton
  dt = 1E3
  end_time = 1E4
[]

[Postprocessors]
  [p000]
    type = PointValue
    variable = pp
    point = '0 0 0'
    execute_on = 'initial timestep_end'
  []
  [p010]
    type = PointValue
    variable = pp
    point = '10 0 0'
    execute_on = 'initial timestep_end'
  []
  [p020]
    type = PointValue
    variable = pp
    point = '20 0 0'
    execute_on = 'initial timestep_end'
  []
  [p030]
    type = PointValue
    variable = pp
    point = '30 0 0'
    execute_on = 'initial timestep_end'
  []
  [p040]
    type = PointValue
    variable = pp
    point = '40 0 0'
    execute_on = 'initial timestep_end'
  []
  [p050]
    type = PointValue
    variable = pp
    point = '50 0 0'
    execute_on = 'initial timestep_end'
  []
  [p060]
    type = PointValue
    variable = pp
    point = '60 0 0'
    execute_on = 'initial timestep_end'
  []
  [p070]
    type = PointValue
    variable = pp
    point = '70 0 0'
    execute_on = 'initial timestep_end'
  []
  [p080]
    type = PointValue
    variable = pp
    point = '80 0 0'
    execute_on = 'initial timestep_end'
  []
  [p090]
    type = PointValue
    variable = pp
    point = '90 0 0'
    execute_on = 'initial timestep_end'
  []
  [p100]
    type = PointValue
    variable = pp
    point = '100 0 0'
    execute_on = 'initial timestep_end'
  []
[]

[Outputs]
  file_base = pressure_pulse_1d
  print_linear_residuals = false
  csv = true
[]

(modules/porous_flow/test/tests/pressure_pulse/pressure_pulse_1d_3comp_action.i)

# Pressure pulse in 1D with 1 phase but 3 components (viscosity, relperm, etc are independent of mass-fractions) - transient
# This input file uses the PorousFlowFullySaturated Action.  For the non-Action version, see pressure_pulse_1d_3comp.i
[Mesh]
  type = GeneratedMesh
  dim = 1
  nx = 10
  xmin = 0
  xmax = 100
[]

[GlobalParams]
  PorousFlowDictator = dictator
[]

[Variables]
  [pp]
    initial_condition = 2E6
  []
  [massfrac0]
    initial_condition = 0.1
  []
  [massfrac1]
    initial_condition = 0.3
  []
[]

[PorousFlowFullySaturated]
  porepressure = pp
  mass_fraction_vars = 'massfrac0 massfrac1'
  gravity = '0 0 0'
  fp = simple_fluid
  stabilization = Full
[]

[Modules]
  [FluidProperties]
    [simple_fluid]
      type = SimpleFluidProperties
      bulk_modulus = 2e9
      density0 = 1000
      thermal_expansion = 0
      viscosity = 1e-3
    []
  []
[]

[Materials]
  [porosity]
    type = PorousFlowPorosityConst
    porosity = 0.1
  []
  [permeability]
    type = PorousFlowPermeabilityConst
    permeability = '1E-15 0 0 0 1E-15 0 0 0 1E-15'
  []
[]

[BCs]
  [left]
    type = DirichletBC
    boundary = left
    value = 3E6
    variable = pp
  []
[]

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

[Executioner]
  type = Transient
  solve_type = Newton
  dt = 1E3
  end_time = 1E4
[]

[Postprocessors]
  [p000]
    type = PointValue
    variable = pp
    point = '0 0 0'
    execute_on = 'initial timestep_end'
  []
  [p010]
    type = PointValue
    variable = pp
    point = '10 0 0'
    execute_on = 'initial timestep_end'
  []
  [p020]
    type = PointValue
    variable = pp
    point = '20 0 0'
    execute_on = 'initial timestep_end'
  []
  [p030]
    type = PointValue
    variable = pp
    point = '30 0 0'
    execute_on = 'initial timestep_end'
  []
  [p040]
    type = PointValue
    variable = pp
    point = '40 0 0'
    execute_on = 'initial timestep_end'
  []
  [p050]
    type = PointValue
    variable = pp
    point = '50 0 0'
    execute_on = 'initial timestep_end'
  []
  [p060]
    type = PointValue
    variable = pp
    point = '60 0 0'
    execute_on = 'initial timestep_end'
  []
  [p070]
    type = PointValue
    variable = pp
    point = '70 0 0'
    execute_on = 'initial timestep_end'
  []
  [p080]
    type = PointValue
    variable = pp
    point = '80 0 0'
    execute_on = 'initial timestep_end'
  []
  [p090]
    type = PointValue
    variable = pp
    point = '90 0 0'
    execute_on = 'initial timestep_end'
  []
  [p100]
    type = PointValue
    variable = pp
    point = '100 0 0'
    execute_on = 'initial timestep_end'
  []
  [mf_0_010]
    type = PointValue
    variable = massfrac0
    point = '10 0 0'
    execute_on = 'timestep_end'
  []
  [mf_1_010]
    type = PointValue
    variable = massfrac1
    point = '10 0 0'
    execute_on = 'timestep_end'
  []
[]

[Outputs]
  file_base = pressure_pulse_1d_3comp
  print_linear_residuals = true
  csv = true
[]

(modules/porous_flow/test/tests/pressure_pulse/pressure_pulse_1d_2phase.i)

# Pressure pulse in 1D with 2 phases (with one having zero saturation), 2components - transient
[Mesh]
  type = GeneratedMesh
  dim = 1
  nx = 10
  xmin = 0
  xmax = 100
[]

[GlobalParams]
  PorousFlowDictator = dictator
[]

[Variables]
  [ppwater]
    initial_condition = 2E6
  []
  [ppgas]
    initial_condition = 2E6
  []
[]

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

[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
  []
[]

[Modules]
  [FluidProperties]
    [simple_fluid0]
      type = SimpleFluidProperties
      bulk_modulus = 2e9
      density0 = 1000
      thermal_expansion = 0
      viscosity = 1e-3
    []
    [simple_fluid1]
      type = SimpleFluidProperties
      bulk_modulus = 2e6
      density0 = 1
      thermal_expansion = 0
      viscosity = 1e-5
    []
  []
[]

[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 = '1E-15 0 0 0 1E-15 0 0 0 1E-15'
  []
  [relperm_water]
    type = PorousFlowRelativePermeabilityCorey
    n = 1
    phase = 0
  []
  [relperm_gas]
    type = PorousFlowRelativePermeabilityCorey
    n = 1
    phase = 1
  []
[]

[BCs]
  [leftwater]
    type = DirichletBC
    boundary = left
    value = 3E6
    variable = ppwater
  []
  [leftgas]
    type = DirichletBC
    boundary = left
    value = 3E6
    variable = ppgas
  []
[]

[Preconditioning]
  [andy]
    type = SMP
    full = true
    petsc_options = '-snes_converged_reason -ksp_diagonal_scale -ksp_diagonal_scale_fix -ksp_gmres_modifiedgramschmidt -snes_linesearch_monitor'
    petsc_options_iname = '-ksp_type -pc_type -sub_pc_type -sub_pc_factor_shift_type -pc_asm_overlap -snes_atol -snes_rtol -snes_max_it'
    petsc_options_value = 'gmres      asm      lu           NONZERO                   2               1E-15       1E-20 20'
  []
[]

[Executioner]
  type = Transient
  solve_type = Newton
  dt = 1E3
  end_time = 1E4
[]

[Postprocessors]
  [p000]
    type = PointValue
    variable = ppwater
    point = '0 0 0'
    execute_on = 'initial timestep_end'
  []
  [p010]
    type = PointValue
    variable = ppwater
    point = '10 0 0'
    execute_on = 'initial timestep_end'
  []
  [p020]
    type = PointValue
    variable = ppwater
    point = '20 0 0'
    execute_on = 'initial timestep_end'
  []
  [p030]
    type = PointValue
    variable = ppwater
    point = '30 0 0'
    execute_on = 'initial timestep_end'
  []
  [p040]
    type = PointValue
    variable = ppwater
    point = '40 0 0'
    execute_on = 'initial timestep_end'
  []
  [p050]
    type = PointValue
    variable = ppwater
    point = '50 0 0'
    execute_on = 'initial timestep_end'
  []
  [p060]
    type = PointValue
    variable = ppwater
    point = '60 0 0'
    execute_on = 'initial timestep_end'
  []
  [p070]
    type = PointValue
    variable = ppwater
    point = '70 0 0'
    execute_on = 'initial timestep_end'
  []
  [p080]
    type = PointValue
    variable = ppwater
    point = '80 0 0'
    execute_on = 'initial timestep_end'
  []
  [p090]
    type = PointValue
    variable = ppwater
    point = '90 0 0'
    execute_on = 'initial timestep_end'
  []
  [p100]
    type = PointValue
    variable = ppwater
    point = '100 0 0'
    execute_on = 'initial timestep_end'
  []
[]

[Outputs]
  file_base = pressure_pulse_1d_2phase
  print_linear_residuals = false
  csv = true
[]

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Pressure-pulses in 1D