PorousFlowFullySaturatedAdvectiveFlux

Fully-upwinded advective flux of the fluid component given by fluid_component, in a single-phase fluid

Describes the differential term $var element = document.getElementById("moose-equation-9a3db2d1-96eb-4c43-88be-89fc9c88b08b");katex.render("-\\nabla\\cdot ((\\rho)\\chi^{\\kappa} k(\\nabla P - \\rho \\mathbf{g})/\\mu) \\ .", element, {displayMode:true,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ The nomenclature is described here. This is fully-saturated, multi-component, single-phase Darcy flow for fluid component $var element = document.getElementById("moose-equation-4befe6fb-d7ab-4e2a-88e1-07d81e726099");katex.render("\\kappa", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ .

The factor $var element = document.getElementById("moose-equation-cca40b64-9612-4317-9c6a-411fede18095");katex.render("(\\rho)", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ appears in parentheses because it is optional and controlled by the multiply_by_density flag. If multiply_by_density = false is chosen then the problem becomes more linear (and hence converges faster) but care must be taken with other PorousFlow objects (such as PorousFlowFluidMass) since all fluxes become volume fluxes (with SI units m $var element = document.getElementById("moose-equation-6b40db74-fcbe-4100-a774-22c0b9c734ad");katex.render("^{3}", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ .m $var element = document.getElementById("moose-equation-69af5387-3664-4757-bf84-f0d899af08ea");katex.render("^{-3}", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ .s $var element = document.getElementById("moose-equation-34118f67-d78f-45f1-b4e1-1cd8c7a810b2");katex.render("^{-1}", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ ) instead of the usual mass fluxes (with SI units kg.m $var element = document.getElementById("moose-equation-21d0eb90-0cfa-4181-bb42-038f504ab3c7");katex.render("^{-3}", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ .s $var element = document.getElementById("moose-equation-dc805761-c857-42e5-a16e-02594e92a51e");katex.render("^{-1}", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ )

Full upwinding is used in this Kernel. See the numerical stabilization lead page page for more details.

This Kernel may be added automatically by the PorousFlowFullySaturated Action: see more discussion on that page.

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
gravityGravitational acceleration vector downwards (m/s^2)
C++ Type:libMesh::VectorValue<double>
Unit:(no unit assumed)
Controllable:No
Description:Gravitational acceleration vector downwards (m/s^2)
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
fallback_schemequickquick: use nodal mobility without preserving mass. harmonic: use a harmonic mean of nodal mobilities and preserve fluid mass
Default:quick
C++ Type:MooseEnum
Unit:(no unit assumed)
Options:quick, harmonic
Controllable:No
Description:quick: use nodal mobility without preserving mass. harmonic: use a harmonic mean of nodal mobilities and preserve fluid mass
fluid_component0The index corresponding to the fluid component for this kernel
Default:0
C++ Type:unsigned int
Unit:(no unit assumed)
Controllable:No
Description:The index corresponding to the fluid component for this kernel
full_upwind_threshold5If, for each timestep, the number of upwind-downwind swaps in an element is less than this quantity, then full upwinding is used for that element. Otherwise the fallback scheme is employed.
Default:5
C++ Type:unsigned int
Unit:(no unit assumed)
Controllable:No
Description:If, for each timestep, the number of upwind-downwind swaps in an element is less than this quantity, then full upwinding is used for that element. Otherwise the fallback scheme is employed.
multiply_by_densityTrueIf true, then this Kernel is the fluid mass flux. If false, then this Kernel is the fluid volume flux (which is common in poro-mechanics)
Default:True
C++ Type:bool
Unit:(no unit assumed)
Controllable:No
Description:If true, then this Kernel is the fluid mass flux. If false, then this Kernel is the fluid volume flux (which is common in poro-mechanics)
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/fflux02_fully_saturated.i)
(modules/porous_flow/test/tests/gravity/fully_saturated_upwinded_grav01c.i)

References

No citations exist within this document.

(modules/porous_flow/test/tests/jacobian/fflux02_fully_saturated.i)

# Using PorousFlowFullySaturatedAdvectiveFlux
# 1phase, 3components, constant insitu permeability
# density with constant bulk, constant viscosity, nonzero gravity
[Mesh]
  type = GeneratedMesh
  dim = 1
  nx = 1
[]

[GlobalParams]
  PorousFlowDictator = dictator
[]

[Variables]
  [pp]
  []
  [massfrac0]
  []
  [massfrac1]
  []
[]

[ICs]
  [pp]
    type = FunctionIC
    variable = pp
    function = -0.7+x+y
  []
  [massfrac0]
    type = RandomIC
    variable = massfrac0
    min = 0
    max = 0.3
  []
  [massfrac1]
    type = RandomIC
    variable = massfrac1
    min = 0
    max = 0.4
  []
[]

[Kernels]
  [flux0]
    type = PorousFlowFullySaturatedAdvectiveFlux
    fluid_component = 0
    variable = pp
    gravity = '-1 -0.1 0'
  []
  [flux1]
    type = PorousFlowFullySaturatedAdvectiveFlux
    fluid_component = 1
    variable = massfrac0
    gravity = '-1 -0.1 0'
  []
  [flux2]
    type = PorousFlowFullySaturatedAdvectiveFlux
    fluid_component = 2
    variable = massfrac1
    gravity = '-1 -0.1 0'
  []
  [flux0_nodensity]
    type = PorousFlowFullySaturatedAdvectiveFlux
    fluid_component = 0
    variable = pp
    gravity = '-1 -0.1 0'
    multiply_by_density = false
  []
  [flux1_nodensity]
    type = PorousFlowFullySaturatedAdvectiveFlux
    fluid_component = 1
    variable = massfrac0
    gravity = '-1 -0.1 0'
    multiply_by_density = false
  []
  [flux2_nodensity]
    type = PorousFlowFullySaturatedAdvectiveFlux
    fluid_component = 2
    variable = massfrac1
    gravity = '-1 -0.1 0'
    multiply_by_density = false
  []
[]

[UserObjects]
  [dictator]
    type = PorousFlowDictator
    porous_flow_vars = 'pp massfrac0 massfrac1'
    number_fluid_phases = 1
    number_fluid_components = 3
  []
[]

[FluidProperties]
  [simple_fluid]
    type = SimpleFluidProperties
    bulk_modulus = 1.5
    density0 = 1
    thermal_expansion = 0
    viscosity = 1
  []
[]

[Materials]
  [temperature]
    type = PorousFlowTemperature
  []
  [ppss]
    type = PorousFlow1PhaseFullySaturated
    porepressure = pp
  []
  [massfrac]
    type = PorousFlowMassFraction
    mass_fraction_vars = 'massfrac0 massfrac1'
  []
  [simple_fluid]
    type = PorousFlowSingleComponentFluid
    fp = simple_fluid
    phase = 0
  []
  [permeability]
    type = PorousFlowPermeabilityConst
    permeability = '2 0 0 0 2 0 0 0 3'
  []
[]

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

[Executioner]
  type = Transient
  solve_type = Newton
  dt = 1
  num_steps = 1
[]

(modules/porous_flow/test/tests/gravity/fully_saturated_upwinded_grav01c.i)

# Checking that gravity head is established
# 1phase, 2-component, constant fluid-bulk, constant viscosity, constant permeability
# fully saturated with fully-saturated Kernel with upwinding
# For better agreement with the analytical solution (ana_pp), just increase nx
# NOTE: this test is numerically delicate because the steady-state configuration is independent of the mass fraction, so the frac variable can assume any value as long as mass-fraction is conserved

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

[GlobalParams]
  PorousFlowDictator = dictator
[]

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

[Kernels]
  [flux1]
    type = PorousFlowFullySaturatedAdvectiveFlux
    variable = pp
    fluid_component = 1
    gravity = '-1 0 0'
  []
  [flux0]
    type = PorousFlowFullySaturatedAdvectiveFlux
    variable = frac
    fluid_component = 0
    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 frac'
    number_fluid_phases = 1
    number_fluid_components = 2
  []
[]

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

[Materials]
  [temperature]
    type = PorousFlowTemperature
  []
  [ppss]
    type = PorousFlow1PhaseFullySaturated
    porepressure = pp
  []
  [massfrac]
    type = PorousFlowMassFraction
    mass_fraction_vars = frac
  []
  [simple_fluid]
    type = PorousFlowSingleComponentFluid
    fp = simple_fluid
    phase = 0
  []
  [permeability]
    type = PorousFlowPermeabilityConst
    permeability = '1 0 0  0 2 0  0 0 3'
  []
[]

[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
  nl_rel_tol = 1E-12
  petsc_options_iname = '-pc_factor_shift_type'
  petsc_options_value = 'NONZERO'
  nl_max_its = 100
[]

[Outputs]
  csv = true
[]

Input Parameters
Input Files
References