PorousFlowBasicAdvection

Advective flux of a Variable using the Darcy velocity of the fluid phase

This Kernel implements the differential expression $var element = document.getElementById("moose-equation-b94be91a-5e26-46fa-bd9e-6f4c7cbdab45");katex.render("\\nabla\\cdot(\\mathbf{v}_{\\beta} u) \\ ,", element, {displayMode:true,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ where $var element = document.getElementById("moose-equation-5c434c3c-c5d6-4efd-aa14-e26ecb167965");katex.render("\\mathbf{v}_{\\beta}", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ is Darcy velocity of fluid phase $var element = document.getElementById("moose-equation-25c79180-281f-46e5-8953-2ebd0f016a2c");katex.render("\\beta", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ . That is, the advection of a variable $var element = document.getElementById("moose-equation-954dbe1a-6bcd-41af-a671-d08a4fb6d492");katex.render("u", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ . The Darcy velocity is defined to be $var element = document.getElementById("moose-equation-aa2ce8eb-2365-40f6-be21-2df5d6be74b9");katex.render("\\mathbf{v}_{\\beta} = -\\frac{k k_{\\mathrm{r,}\\ \\beta}}{\\mu_{\\beta}}(\\nabla P_{\\beta} - \\rho_{\\beta}\\mathbf{g}) \\ ,", element, {displayMode:true,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ where $var element = document.getElementById("moose-equation-0642246e-94cd-41fc-a445-fad55eb2480e");katex.render("k", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ is the permeability tensor, $var element = document.getElementById("moose-equation-1a5384aa-aa70-4605-8be4-e25ffd174b31");katex.render("k_{\\mathrm{r,}\\ \\beta}", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ is the relative permeability, $var element = document.getElementById("moose-equation-d2ec05d4-4d66-4508-b373-d8a453f063d0");katex.render("\\mu", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ is the viscosity, $var element = document.getElementById("moose-equation-224f2e0f-32f5-4355-be60-ca4662679045");katex.render("P", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ is the porepressure, $var element = document.getElementById("moose-equation-5adaffe9-6964-454b-80f7-714d0a5ddb0f");katex.render("\\rho", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ is the density and $var element = document.getElementById("moose-equation-30907915-5cde-489a-b11e-70dfa941165b");katex.render("\\mathbf{g}", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ is the gravitational acceleration.

This Kernel is designed to be used with tracers or other similar variables that are not described by the mass fraction variables of PorousFlow. It requires the use of the PorousFlowDarcyVelocityMaterial material.

warning

The most naive implementation of advection is used. You will almost definitely see spurious overshoots and undershoots as well as numerical diffusion when using this Kernel. It is usually better to use the PorousFlowAdvectiveFlux if possible.

The typical usage of this Kernel is to model the advection equation $var element = document.getElementById("moose-equation-850b1ec5-fd3f-4e00-b3c4-1933c5541877");katex.render("\\dot{u}+\\nabla (vu) = 0", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ , which is implemented by the following:

[Kernels]
  [u_dot]
    type = TimeDerivative
    variable = u
  []
  [u_advection]
    type = PorousFlowBasicAdvection
    variable = u
    phase = 0
  []
[]

Input Parameters

PorousFlowDictatorThe UserObject that holds the list of PorousFlow variable names.
C++ Type:UserObjectName
Unit:(no unit assumed)
Controllable:No
Description:The UserObject that holds the list of PorousFlow variable names.
variableThe name of the variable that this residual object operates on
C++ Type:NonlinearVariableName
Unit:(no unit assumed)
Controllable:No
Description:The name of the variable that this residual object operates on

Required Parameters

blockThe list of blocks (ids or names) that this object will be applied
C++ Type:std::vector<SubdomainName>
Unit:(no unit assumed)
Controllable:No
Description:The list of blocks (ids or names) that this object will be applied
displacementsThe displacements
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:The displacements
phase0Use the Darcy velocity of this fluid phase
Default:0
C++ Type:unsigned int
Unit:(no unit assumed)
Controllable:No
Description:Use the Darcy velocity of this fluid phase
prop_getter_suffixAn optional suffix parameter that can be appended to any attempt to retrieve/get material properties. The suffix will be prepended with a '_' character.
C++ Type:MaterialPropertyName
Unit:(no unit assumed)
Controllable:No
Description:An optional suffix parameter that can be appended to any attempt to retrieve/get material properties. The suffix will be prepended with a '_' character.
use_interpolated_stateFalseFor the old and older state use projected material properties interpolated at the quadrature points. To set up projection use the ProjectedStatefulMaterialStorageAction.
Default:False
C++ Type:bool
Unit:(no unit assumed)
Controllable:No
Description:For the old and older state use projected material properties interpolated at the quadrature points. To set up projection use the ProjectedStatefulMaterialStorageAction.

Optional Parameters

absolute_value_vector_tagsThe tags for the vectors this residual object should fill with the absolute value of the residual contribution
C++ Type:std::vector<TagName>
Unit:(no unit assumed)
Controllable:No
Description:The tags for the vectors this residual object should fill with the absolute value of the residual contribution
extra_matrix_tagsThe extra tags for the matrices this Kernel should fill
C++ Type:std::vector<TagName>
Unit:(no unit assumed)
Controllable:No
Description:The extra tags for the matrices this Kernel should fill
extra_vector_tagsThe extra tags for the vectors this Kernel should fill
C++ Type:std::vector<TagName>
Unit:(no unit assumed)
Controllable:No
Description:The extra tags for the vectors this Kernel should fill
matrix_tagssystemThe tag for the matrices this Kernel should fill
Default:system
C++ Type:MultiMooseEnum
Unit:(no unit assumed)
Options:nontime, system
Controllable:No
Description:The tag for the matrices this Kernel should fill
vector_tagsnontimeThe tag for the vectors this Kernel should fill
Default:nontime
C++ Type:MultiMooseEnum
Unit:(no unit assumed)
Options:nontime, time
Controllable:No
Description:The tag for the vectors this Kernel should fill

Tagging Parameters

control_tagsAdds user-defined labels for accessing object parameters via control logic.
C++ Type:std::vector<std::string>
Unit:(no unit assumed)
Controllable:No
Description:Adds user-defined labels for accessing object parameters via control logic.
diag_save_inThe name of auxiliary variables to save this Kernel's diagonal Jacobian contributions to. Everything about that variable must match everything about this variable (the type, what blocks it's on, etc.)
C++ Type:std::vector<AuxVariableName>
Unit:(no unit assumed)
Controllable:No
Description:The name of auxiliary variables to save this Kernel's diagonal Jacobian contributions to. Everything about that variable must match everything about this variable (the type, what blocks it's on, etc.)
enableTrueSet the enabled status of the MooseObject.
Default:True
C++ Type:bool
Unit:(no unit assumed)
Controllable:Yes
Description:Set the enabled status of the MooseObject.
implicitTrueDetermines whether this object is calculated using an implicit or explicit form
Default:True
C++ Type:bool
Unit:(no unit assumed)
Controllable:No
Description:Determines whether this object is calculated using an implicit or explicit form
save_inThe name of auxiliary variables to save this Kernel's residual contributions to. Everything about that variable must match everything about this variable (the type, what blocks it's on, etc.)
C++ Type:std::vector<AuxVariableName>
Unit:(no unit assumed)
Controllable:No
Description:The name of auxiliary variables to save this Kernel's residual contributions to. Everything about that variable must match everything about this variable (the type, what blocks it's on, etc.)
seed0The seed for the master random number generator
Default:0
C++ Type:unsigned int
Unit:(no unit assumed)
Controllable:No
Description:The seed for the master random number generator
use_displaced_meshFalseWhether or not this object should use the displaced mesh for computation. Note that in the case this is true but no displacements are provided in the Mesh block the undisplaced mesh will still be used.
Default:False
C++ Type:bool
Unit:(no unit assumed)
Controllable:No
Description:Whether or not this object should use the displaced mesh for computation. Note that in the case this is true but no displacements are provided in the Mesh block the undisplaced mesh will still be used.

Advanced Parameters

Input Files

(modules/porous_flow/test/tests/jacobian/basic_advection4.i)
(modules/porous_flow/test/tests/basic_advection/1phase.i)
(modules/porous_flow/test/tests/basic_advection/except2.i)
(modules/porous_flow/test/tests/jacobian/basic_advection1.i)
(modules/porous_flow/test/tests/jacobian/basic_advection6.i)
(modules/porous_flow/test/tests/jacobian/basic_advection2.i)
(modules/porous_flow/test/tests/jacobian/basic_advection3.i)
(modules/porous_flow/test/tests/basic_advection/2phase.i)
(modules/porous_flow/test/tests/basic_advection/except1.i)
(modules/porous_flow/test/tests/jacobian/basic_advection5.i)

(modules/porous_flow/test/tests/basic_advection/1phase.i)

# Basic advection of u in a 1-phase situation
#
# grad(P) = -2
# density * gravity = 4 * 0.25
# grad(P) - density * gravity = -3
# permeability = 5
# viscosity = 150
# so Darcy velocity = 0.1
[Mesh]
  type = GeneratedMesh
  dim = 1
  nx = 10
  xmin = 0
  xmax = 1
[]

[GlobalParams]
  PorousFlowDictator = dictator
[]

[Variables]
  [u]
  []
[]

[AuxVariables]
  [P]
  []
[]

[ICs]
  [P]
    type = FunctionIC
    variable = P
    function = '2*(1-x)'
  []
  [u]
    type = FunctionIC
    variable = u
    function = 'if(x<0.1,1,0)'
  []
[]

[Kernels]
  [u_dot]
    type = TimeDerivative
    variable = u
  []
  [u_advection]
    type = PorousFlowBasicAdvection
    variable = u
    phase = 0
  []
[]

[UserObjects]
  [dictator]
    type = PorousFlowDictator
    porous_flow_vars = ''
    number_fluid_phases = 1
    number_fluid_components = 1
  []
  [pc]
    type = PorousFlowCapillaryPressureConst
  []
[]

[FluidProperties]
  [simple_fluid]
    type = SimpleFluidProperties
    bulk_modulus = 2e9
    density0 = 4
    thermal_expansion = 0
    viscosity = 150.0
  []
[]

[Materials]
  [temperature]
    type = PorousFlowTemperature
  []
  [ppss]
    type = PorousFlow1PhaseP
    porepressure = P
    capillary_pressure = pc
  []
  [simple_fluid]
    type = PorousFlowSingleComponentFluid
    fp = simple_fluid
    phase = 0
  []
  [permeability]
    type = PorousFlowPermeabilityConst
    permeability = '5 0 0 0 5 0 0 0 5'
  []
  [relperm]
    type = PorousFlowRelativePermeabilityCorey
    n = 0
    phase = 0
  []
  [darcy_velocity]
    type = PorousFlowDarcyVelocityMaterial
    gravity = '0.25 0 0'
  []
[]

[BCs]
  [left]
    type = DirichletBC
    boundary = left
    value = 1
    variable = u
  []
  [right]
    type = DirichletBC
    boundary = right
    value = 0
    variable = u
  []
[]

[Preconditioning]
  [basic]
    type = SMP
    full = true
    petsc_options_iname = '-pc_type -snes_rtol'
    petsc_options_value = ' lu       1E-10'
  []
[]

[Executioner]
  type = Transient
  solve_type = Newton
  dt = 1
  end_time = 5
[]

[Outputs]
  exodus = true
  print_linear_residuals = false
[]

(modules/porous_flow/test/tests/jacobian/basic_advection4.i)

# Basic advection with 1 porepressure and temperature as PorousFlow variables
# Constant permeability
[Mesh]
  type = GeneratedMesh
  dim = 1
  nx = 1
[]

[GlobalParams]
  PorousFlowDictator = dictator
[]

[Variables]
  [u]
  []
  [T]
  []
  [P]
  []
[]

[ICs]
  [P]
    type = RandomIC
    variable = P
    min = 2E5
    max = 4E5
  []
  [T]
    type = RandomIC
    variable = T
    min = 300
    max = 900
  []
  [u]
    type = RandomIC
    variable = u
  []
[]

[Kernels]
  [dummy_T]
    type = NullKernel
    variable = T
  []
  [dummy_P]
    type = NullKernel
    variable = P
  []
  [u_advection]
    type = PorousFlowBasicAdvection
    variable = u
    phase = 0
  []
[]

[UserObjects]
  [dictator]
    type = PorousFlowDictator
    porous_flow_vars = 'P T'
    number_fluid_phases = 1
    number_fluid_components = 1
  []
  [pc]
    type = PorousFlowCapillaryPressureVG
    alpha = 1E-5
    m = 0.6
    sat_lr = 0.1
  []
[]

[FluidProperties]
  [methane]
    type = MethaneFluidProperties
  []
[]

[Materials]
  [temperature_qp]
    type = PorousFlowTemperature
    temperature = T
  []
  [ppss_qp]
    type = PorousFlow1PhaseP
    porepressure = P
    capillary_pressure = pc
  []
  [fluid_qp]
    type = PorousFlowSingleComponentFluid
    fp = methane
    phase = 0
  []
  [permeability]
    type = PorousFlowPermeabilityConst
    permeability = '5 0 0 0 5 0 0 0 5'
  []
  [relperm_qp]
    type = PorousFlowRelativePermeabilityCorey
    n = 2
    phase = 0
    s_res = 0.1
    sum_s_res = 0.1
  []
  [darcy_velocity_qp]
    type = PorousFlowDarcyVelocityMaterial
    gravity = '0.25 0 0'
  []
[]

[Preconditioning]
  [check]
    type = SMP
    full = true
    #petsc_options = '-snes_test_display'
    petsc_options_iname = '-snes_type'
    petsc_options_value = ' test'
  []
[]

[Executioner]
  type = Transient
  solve_type = Newton
  end_time = 1
[]

(modules/porous_flow/test/tests/basic_advection/1phase.i)

# Basic advection of u in a 1-phase situation
#
# grad(P) = -2
# density * gravity = 4 * 0.25
# grad(P) - density * gravity = -3
# permeability = 5
# viscosity = 150
# so Darcy velocity = 0.1
[Mesh]
  type = GeneratedMesh
  dim = 1
  nx = 10
  xmin = 0
  xmax = 1
[]

[GlobalParams]
  PorousFlowDictator = dictator
[]

[Variables]
  [u]
  []
[]

[AuxVariables]
  [P]
  []
[]

[ICs]
  [P]
    type = FunctionIC
    variable = P
    function = '2*(1-x)'
  []
  [u]
    type = FunctionIC
    variable = u
    function = 'if(x<0.1,1,0)'
  []
[]

[Kernels]
  [u_dot]
    type = TimeDerivative
    variable = u
  []
  [u_advection]
    type = PorousFlowBasicAdvection
    variable = u
    phase = 0
  []
[]

[UserObjects]
  [dictator]
    type = PorousFlowDictator
    porous_flow_vars = ''
    number_fluid_phases = 1
    number_fluid_components = 1
  []
  [pc]
    type = PorousFlowCapillaryPressureConst
  []
[]

[FluidProperties]
  [simple_fluid]
    type = SimpleFluidProperties
    bulk_modulus = 2e9
    density0 = 4
    thermal_expansion = 0
    viscosity = 150.0
  []
[]

[Materials]
  [temperature]
    type = PorousFlowTemperature
  []
  [ppss]
    type = PorousFlow1PhaseP
    porepressure = P
    capillary_pressure = pc
  []
  [simple_fluid]
    type = PorousFlowSingleComponentFluid
    fp = simple_fluid
    phase = 0
  []
  [permeability]
    type = PorousFlowPermeabilityConst
    permeability = '5 0 0 0 5 0 0 0 5'
  []
  [relperm]
    type = PorousFlowRelativePermeabilityCorey
    n = 0
    phase = 0
  []
  [darcy_velocity]
    type = PorousFlowDarcyVelocityMaterial
    gravity = '0.25 0 0'
  []
[]

[BCs]
  [left]
    type = DirichletBC
    boundary = left
    value = 1
    variable = u
  []
  [right]
    type = DirichletBC
    boundary = right
    value = 0
    variable = u
  []
[]

[Preconditioning]
  [basic]
    type = SMP
    full = true
    petsc_options_iname = '-pc_type -snes_rtol'
    petsc_options_value = ' lu       1E-10'
  []
[]

[Executioner]
  type = Transient
  solve_type = Newton
  dt = 1
  end_time = 5
[]

[Outputs]
  exodus = true
  print_linear_residuals = false
[]

(modules/porous_flow/test/tests/basic_advection/except2.i)

# PorousFlowDarcyVelocityMaterial attempts to have at_nodes = true
[Mesh]
  type = GeneratedMesh
  dim = 1
  nx = 100
  xmin = 0
  xmax = 1
[]

[GlobalParams]
  PorousFlowDictator = dictator
[]

[Variables]
  [u]
  []
[]

[AuxVariables]
  [P]
  []
[]

[ICs]
  [P]
    type = FunctionIC
    variable = P
    function = '2*(1-x)'
  []
  [u]
    type = FunctionIC
    variable = u
    function = 'if(x<0.1,1,0)'
  []
[]

[Kernels]
  [u_dot]
    type = TimeDerivative
    variable = u
  []
  [u_advection]
    type = PorousFlowBasicAdvection
    variable = u
    phase = 1
  []
[]

[UserObjects]
  [dictator]
    type = PorousFlowDictator
    porous_flow_vars = ''
    number_fluid_phases = 1
    number_fluid_components = 1
  []
  [pc]
    type = PorousFlowCapillaryPressureConst
  []
[]

[FluidProperties]
  [simple_fluid]
    type = SimpleFluidProperties
    bulk_modulus = 2e9
    density0 = 4
    thermal_expansion = 0
    viscosity = 150.0
  []
[]

[Materials]
  [temperature]
    type = PorousFlowTemperature
  []
  [ppss]
    type = PorousFlow1PhaseP
    porepressure = P
    capillary_pressure = pc
  []
  [simple_fluid]
    type = PorousFlowSingleComponentFluid
    fp = simple_fluid
    phase = 0
  []
  [permeability]
    type = PorousFlowPermeabilityConst
    permeability = '5 0 0 0 5 0 0 0 5'
  []
  [relperm]
    type = PorousFlowRelativePermeabilityCorey
    n = 0
    phase = 0
  []
  [darcy_velocity]
    type = PorousFlowDarcyVelocityMaterial
    gravity = '0.25 0 0'
    at_nodes = true
  []
[]

[BCs]
  [left]
    type = DirichletBC
    boundary = left
    value = 1
    variable = u
  []
  [right]
    type = DirichletBC
    boundary = right
    value = 0
    variable = u
  []
[]

[Preconditioning]
  [basic]
    type = SMP
    full = true
    petsc_options_iname = '-pc_type -snes_rtol'
    petsc_options_value = ' lu       1E-10'
  []
[]

[Executioner]
  type = Transient
  solve_type = Newton
  dt = 1
  end_time = 5
[]

[Outputs]
  exodus = true
  print_linear_residuals = false
[]

(modules/porous_flow/test/tests/jacobian/basic_advection1.i)

# Basic advection with no PorousFlow variables
[Mesh]
  type = GeneratedMesh
  dim = 1
  nx = 1
[]

[GlobalParams]
  PorousFlowDictator = dictator
[]

[Variables]
  [u]
  []
[]

[AuxVariables]
  [P]
  []
[]

[ICs]
  [P]
    type = FunctionIC
    variable = P
    function = '2*(1-x)'
  []
  [u]
    type = RandomIC
    variable = u
  []
[]

[Kernels]
  [u_advection]
    type = PorousFlowBasicAdvection
    variable = u
    phase = 0
  []
[]

[UserObjects]
  [dictator]
    type = PorousFlowDictator
    porous_flow_vars = ''
    number_fluid_phases = 1
    number_fluid_components = 1
  []
  [pc]
    type = PorousFlowCapillaryPressureConst
  []
[]

[FluidProperties]
  [simple_fluid]
    type = SimpleFluidProperties
    bulk_modulus = 2e9
    density0 = 4
    thermal_expansion = 0
    viscosity = 150.0
  []
[]

[Materials]
  [temperature_qp]
    type = PorousFlowTemperature
  []
  [ppss_qp]
    type = PorousFlow1PhaseP
    porepressure = P
    capillary_pressure = pc
  []
  [simple_fluid_qp]
    type = PorousFlowSingleComponentFluid
    fp = simple_fluid
    phase = 0
  []
  [permeability]
    type = PorousFlowPermeabilityConst
    permeability = '5 0 0 0 5 0 0 0 5'
  []
  [relperm_qp]
    type = PorousFlowRelativePermeabilityCorey
    n = 0
    phase = 0
  []
  [darcy_velocity_qp]
    type = PorousFlowDarcyVelocityMaterial
    gravity = '0.25 0 0'
  []
[]

[Preconditioning]
  [check]
    type = SMP
    full = true
    #petsc_options = '-snes_test_display'
    petsc_options_iname = '-snes_type'
    petsc_options_value = ' test'
  []
[]

[Executioner]
  type = Transient
  solve_type = Newton
  end_time = 1
[]

(modules/porous_flow/test/tests/jacobian/basic_advection6.i)

# Basic advection with 2 porepressure as PorousFlow variables
[Mesh]
  type = GeneratedMesh
  dim = 1
  nx = 1
[]

[GlobalParams]
  PorousFlowDictator = dictator
[]

[Variables]
  [u]
  []
  [P0]
  []
  [P1]
  []
[]

[ICs]
  [P0]
    type = RandomIC
    variable = P0
    min = -1
    max = 0
  []
  [P1]
    type = RandomIC
    variable = P1
    min = 0
    max = 1
  []
  [u]
    type = RandomIC
    variable = u
  []
[]

[Kernels]
  [dummy_P0]
    type = NullKernel
    variable = P0
  []
  [dummy_P1]
    type = NullKernel
    variable = P1
  []
  [u_advection]
    type = PorousFlowBasicAdvection
    variable = u
    phase = 0
  []
[]

[UserObjects]
  [dictator]
    type = PorousFlowDictator
    porous_flow_vars = 'P0 P1'
    number_fluid_phases = 2
    number_fluid_components = 1
  []
  [pc]
    type = PorousFlowCapillaryPressureVG
    alpha = 1
    m = 0.6
    sat_lr = 0.1
  []
[]

[FluidProperties]
  [simple_fluid0]
    type = SimpleFluidProperties
    bulk_modulus = 3
    density0 = 4
    thermal_expansion = 0
    viscosity = 150.0
  []
  [simple_fluid1]
    type = SimpleFluidProperties
    bulk_modulus = 4
    density0 = 3
    thermal_expansion = 0
    viscosity = 130.0
  []
[]

[Materials]
  [temperature_qp]
    type = PorousFlowTemperature
  []
  [ppss_qp]
    type = PorousFlow2PhasePP
    phase0_porepressure = P0
    phase1_porepressure = P1
    capillary_pressure = pc
  []
  [simple_fluid0_qp]
    type = PorousFlowSingleComponentFluid
    fp = simple_fluid0
    phase = 0
  []
  [simple_fluid1_qp]
    type = PorousFlowSingleComponentFluid
    fp = simple_fluid1
    phase = 1
  []
  [effective_fluid_pressure]
    type = PorousFlowEffectiveFluidPressure
  []
  [porosity]
    type = PorousFlowPorosity
    porosity_zero = 0.1
    fluid = true
    biot_coefficient = 0.5
    solid_bulk = 1
  []
  [permeability]
    type = PorousFlowPermeabilityKozenyCarman
    poroperm_function = kozeny_carman_phi0
    k0 = 5
    m = 2
    n = 2
    phi0 = 0.1
  []
  [relperm0_qp]
    type = PorousFlowRelativePermeabilityCorey
    n = 2
    phase = 0
    s_res = 0.1
    sum_s_res = 0.1
  []
  [relperm1_qp]
    type = PorousFlowRelativePermeabilityCorey
    n = 3
    phase = 1
    s_res = 0.0
    sum_s_res = 0.1
  []
  [darcy_velocity_qp]
    type = PorousFlowDarcyVelocityMaterial
    gravity = '0.25 0 0'
  []
[]

[Preconditioning]
  [check]
    type = SMP
    full = true
    petsc_options = '-snes_test_display'
    petsc_options_iname = '-snes_type'
    petsc_options_value = ' test'
  []
[]

[Executioner]
  type = Transient
  solve_type = Newton
  end_time = 1
[]

(modules/porous_flow/test/tests/jacobian/basic_advection2.i)

# Basic advection with 1 porepressure as a PorousFlow variable
# Fully saturated
# Constant permeability
# Constant viscosity
[Mesh]
  type = GeneratedMesh
  dim = 1
  nx = 1
[]

[GlobalParams]
  PorousFlowDictator = dictator
[]

[Variables]
  [u]
  []
  [P]
  []
[]

[ICs]
  [P]
    type = RandomIC
    variable = P
  []
  [u]
    type = RandomIC
    variable = u
  []
[]

[Kernels]
  [dummy_P]
    type = NullKernel
    variable = P
  []
  [u_advection]
    type = PorousFlowBasicAdvection
    variable = u
    phase = 0
  []
[]

[UserObjects]
  [dictator]
    type = PorousFlowDictator
    porous_flow_vars = P
    number_fluid_phases = 1
    number_fluid_components = 1
  []
  [pc]
    type = PorousFlowCapillaryPressureVG
    alpha = 1
    m = 0.6
    sat_lr = 0.1
  []
[]

[FluidProperties]
  [simple_fluid]
    type = SimpleFluidProperties
    bulk_modulus = 3
    density0 = 4
    thermal_expansion = 0
    viscosity = 150.0
  []
[]

[Materials]
  [temperature_qp]
    type = PorousFlowTemperature
  []
  [ppss_qp]
    type = PorousFlow1PhaseP
    porepressure = P
    capillary_pressure = pc
  []
  [simple_fluid_qp]
    type = PorousFlowSingleComponentFluid
    fp = simple_fluid
    phase = 0
  []
  [permeability]
    type = PorousFlowPermeabilityConst
    permeability = '5 0 0 0 5 0 0 0 5'
  []
  [relperm_qp]
    type = PorousFlowRelativePermeabilityCorey
    n = 2
    phase = 0
    s_res = 0.1
    sum_s_res = 0.1
  []
  [darcy_velocity_qp]
    type = PorousFlowDarcyVelocityMaterial
    gravity = '0.25 0 0'
  []
[]

[Preconditioning]
  [check]
    type = SMP
    full = true
    #petsc_options = '-snes_test_display'
    petsc_options_iname = '-snes_type'
    petsc_options_value = ' test'
  []
[]

[Executioner]
  type = Transient
  solve_type = Newton
  end_time = 1
[]

(modules/porous_flow/test/tests/jacobian/basic_advection3.i)

# Basic advection with 1 porepressure as a PorousFlow variable
# Constant permeability
# Constant viscosity
[Mesh]
  type = GeneratedMesh
  dim = 1
  nx = 1
[]

[GlobalParams]
  PorousFlowDictator = dictator
[]

[Variables]
  [u]
  []
  [P]
  []
[]

[ICs]
  [P]
    type = RandomIC
    variable = P
    min = -1
    max = 0
  []
  [u]
    type = RandomIC
    variable = u
  []
[]

[Kernels]
  [dummy_P]
    type = NullKernel
    variable = P
  []
  [u_advection]
    type = PorousFlowBasicAdvection
    variable = u
    phase = 0
  []
[]

[UserObjects]
  [dictator]
    type = PorousFlowDictator
    porous_flow_vars = P
    number_fluid_phases = 1
    number_fluid_components = 1
  []
  [pc]
    type = PorousFlowCapillaryPressureVG
    alpha = 1
    m = 0.6
    sat_lr = 0.1
  []
[]

[FluidProperties]
  [simple_fluid]
    type = SimpleFluidProperties
    bulk_modulus = 3
    density0 = 4
    thermal_expansion = 0
    viscosity = 150.0
  []
[]

[Materials]
  [temperature_qp]
    type = PorousFlowTemperature
  []
  [ppss_qp]
    type = PorousFlow1PhaseP
    porepressure = P
    capillary_pressure = pc
  []
  [simple_fluid_qp]
    type = PorousFlowSingleComponentFluid
    fp = simple_fluid
    phase = 0
  []
  [permeability]
    type = PorousFlowPermeabilityConst
    permeability = '5 0 0 0 5 0 0 0 5'
  []
  [relperm_qp]
    type = PorousFlowRelativePermeabilityCorey
    n = 2
    phase = 0
    s_res = 0.1
    sum_s_res = 0.1
  []
  [darcy_velocity_qp]
    type = PorousFlowDarcyVelocityMaterial
    gravity = '0.25 0 0'
  []
[]

[Preconditioning]
  [check]
    type = SMP
    full = true
    #petsc_options = '-snes_test_display'
    petsc_options_iname = '-snes_type'
    petsc_options_value = ' test'
  []
[]

[Executioner]
  type = Transient
  solve_type = Newton
  end_time = 1
[]

(modules/porous_flow/test/tests/basic_advection/2phase.i)

# Basic advection of u in a 2-phase situation
#
# grad(P) = -2
# density * gravity = 4 * 0.25
# grad(P) - density * gravity = -3
# permeability = 10
# relative permeability = 0.5
# viscosity = 150
# so Darcy velocity = 0.1
[Mesh]
  type = GeneratedMesh
  dim = 1
  nx = 10
  xmin = 0
  xmax = 1
[]

[GlobalParams]
  PorousFlowDictator = dictator
[]

[Variables]
  [u]
  []
[]

[AuxVariables]
  [P0]
  []
  [P1]
  []
[]

[ICs]
  [P0]
    type = FunctionIC
    variable = P0
    function = '0'
  []
  [P1]
    type = FunctionIC
    variable = P1
    function = '2*(1-x)'
  []
  [u]
    type = FunctionIC
    variable = u
    function = 'if(x<0.1,1,0)'
  []
[]

[Kernels]
  [u_dot]
    type = TimeDerivative
    variable = u
  []
  [u_advection]
    type = PorousFlowBasicAdvection
    variable = u
    phase = 1
  []
[]

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

[FluidProperties]
  [simple_fluid0]
    type = SimpleFluidProperties
    density0 = 32
    viscosity = 123
  []
  [simple_fluid1]
    type = SimpleFluidProperties
    bulk_modulus = 2e9
    density0 = 4
    thermal_expansion = 0
    viscosity = 150.0
  []
[]

[Materials]
  [temperature]
    type = PorousFlowTemperature
  []
  [ppss]
    type = PorousFlow2PhasePP
    phase0_porepressure = P0
    phase1_porepressure = P1
    capillary_pressure = pc
  []
  [simple_fluid0]
    type = PorousFlowSingleComponentFluid
    fp = simple_fluid0
    phase = 0
  []
  [simple_fluid1]
    type = PorousFlowSingleComponentFluid
    fp = simple_fluid1
    phase = 1
  []
  [permeability]
    type = PorousFlowPermeabilityConst
    permeability = '10 0 0 0 10 0 0 0 10'
  []
  [relperm0]
    type = PorousFlowRelativePermeabilityCorey
    n = 2
    phase = 0
  []
  [relperm1]
    type = PorousFlowRelativePermeabilityConst
    kr = 0.5
    phase = 1
  []
  [darcy_velocity]
    type = PorousFlowDarcyVelocityMaterial
    gravity = '0.25 0 0'
  []
[]

[BCs]
  [left]
    type = DirichletBC
    boundary = left
    value = 1
    variable = u
  []
  [right]
    type = DirichletBC
    boundary = right
    value = 0
    variable = u
  []
[]

[Preconditioning]
  [basic]
    type = SMP
    full = true
    petsc_options_iname = '-pc_type -snes_rtol'
    petsc_options_value = ' lu       1E-10'
  []
[]

[Executioner]
  type = Transient
  solve_type = Newton
  dt = 1
  end_time = 5
[]

[Outputs]
  exodus = true
  print_linear_residuals = false
[]

(modules/porous_flow/test/tests/basic_advection/except1.i)

# phase number is too high in PorousFlowBasicAdvection
[Mesh]
  type = GeneratedMesh
  dim = 1
  nx = 100
  xmin = 0
  xmax = 1
[]

[GlobalParams]
  PorousFlowDictator = dictator
[]

[Variables]
  [u]
  []
[]

[AuxVariables]
  [P]
  []
[]

[ICs]
  [P]
    type = FunctionIC
    variable = P
    function = '2*(1-x)'
  []
  [u]
    type = FunctionIC
    variable = u
    function = 'if(x<0.1,1,0)'
  []
[]

[Kernels]
  [u_dot]
    type = TimeDerivative
    variable = u
  []
  [u_advection]
    type = PorousFlowBasicAdvection
    variable = u
    phase = 1
  []
[]

[UserObjects]
  [dictator]
    type = PorousFlowDictator
    porous_flow_vars = ''
    number_fluid_phases = 1
    number_fluid_components = 1
  []
  [pc]
    type = PorousFlowCapillaryPressureConst
  []
[]

[FluidProperties]
  [simple_fluid]
    type = SimpleFluidProperties
    bulk_modulus = 2e9
    density0 = 4
    thermal_expansion = 0
    viscosity = 150.0
  []
[]

[Materials]
  [temperature]
    type = PorousFlowTemperature
  []
  [ppss]
    type = PorousFlow1PhaseP
    porepressure = P
    capillary_pressure = pc
  []
  [simple_fluid]
    type = PorousFlowSingleComponentFluid
    fp = simple_fluid
    phase = 0
  []
  [permeability]
    type = PorousFlowPermeabilityConst
    permeability = '5 0 0 0 5 0 0 0 5'
  []
  [relperm]
    type = PorousFlowRelativePermeabilityCorey
    n = 0
    phase = 0
  []
  [darcy_velocity]
    type = PorousFlowDarcyVelocityMaterial
    gravity = '0.25 0 0'
  []
[]

[BCs]
  [left]
    type = DirichletBC
    boundary = left
    value = 1
    variable = u
  []
  [right]
    type = DirichletBC
    boundary = right
    value = 0
    variable = u
  []
[]

[Preconditioning]
  [basic]
    type = SMP
    full = true
    petsc_options_iname = '-pc_type -snes_rtol'
    petsc_options_value = ' lu       1E-10'
  []
[]

[Executioner]
  type = Transient
  solve_type = Newton
  dt = 1
  end_time = 5
[]

[Outputs]
  exodus = true
  print_linear_residuals = false
[]

(modules/porous_flow/test/tests/jacobian/basic_advection5.i)

# Basic advection with 1 porepressure as a PorousFlow variable
[Mesh]
  type = GeneratedMesh
  dim = 1
  nx = 1
[]

[GlobalParams]
  PorousFlowDictator = dictator
[]

[Variables]
  [u]
  []
  [P]
  []
[]

[ICs]
  [P]
    type = RandomIC
    variable = P
    min = -1
    max = 1
  []
  [u]
    type = RandomIC
    variable = u
  []
[]

[Kernels]
  [dummy_P]
    type = NullKernel
    variable = P
  []
  [u_advection]
    type = PorousFlowBasicAdvection
    variable = u
    phase = 0
  []
[]

[UserObjects]
  [dictator]
    type = PorousFlowDictator
    porous_flow_vars = P
    number_fluid_phases = 1
    number_fluid_components = 1
  []
  [pc]
    type = PorousFlowCapillaryPressureVG
    alpha = 1
    m = 0.6
    sat_lr = 0.1
  []
[]

[FluidProperties]
  [simple_fluid]
    type = SimpleFluidProperties
    bulk_modulus = 3
    density0 = 4
    thermal_expansion = 0
    viscosity = 150.0
  []
[]

[Materials]
  [temperature_qp]
    type = PorousFlowTemperature
  []
  [ppss_qp]
    type = PorousFlow1PhaseP
    porepressure = P
    capillary_pressure = pc
  []
  [simple_fluid_qp]
    type = PorousFlowSingleComponentFluid
    fp = simple_fluid
    phase = 0
  []
  [effective_fluid_pressure]
    type = PorousFlowEffectiveFluidPressure
  []
  [porosity]
    type = PorousFlowPorosity
    porosity_zero = 0.1
    fluid = true
    biot_coefficient = 0.5
    solid_bulk = 1
  []
  [permeability]
    type = PorousFlowPermeabilityKozenyCarman
    poroperm_function = kozeny_carman_phi0
    k0 = 5
    m = 2
    n = 2
    phi0 = 0.1
  []
  [relperm_qp]
    type = PorousFlowRelativePermeabilityCorey
    n = 2
    phase = 0
  []
  [darcy_velocity_qp]
    type = PorousFlowDarcyVelocityMaterial
    gravity = '0.25 0 0'
  []
[]

[Preconditioning]
  [check]
    type = SMP
    full = true
    #petsc_options = '-snes_test_display'
    petsc_options_iname = '-snes_type'
    petsc_options_value = ' test'
  []
[]

[Executioner]
  type = Transient
  solve_type = Newton
  end_time = 1
[]

Input Parameters
Input Files