PorousFlowDarcyVelocityComponentLowerDimensional

Darcy velocity on a lower-dimensional element embedded in a higher-dimensional mesh. Units m^3.s-1.m^{-2, or m.s}-1. Darcy velocity = -(k_ij * krel /(mu * a) (nabla_j P - w_j)), where k_ij is the permeability tensor, krel is the relative permeability, mu is the fluid viscosity, P is the fluid pressure, a is the fracture aperture and w_j is the fluid weight. The difference between this AuxKernel and PorousFlowDarcyVelocity is that this one projects gravity along the element's tangent direction. NOTE! For a meaningful answer, your permeability tensor must NOT contain terms that rotate tangential vectors to non-tangential vectors.

This AuxKernel records the Darcy velocity within a lower-dimensional element living in a higher-dimensional mesh. For instance, to study flow within a fractured material, you might have created a 3D mesh with its own 3D subdomains (blocks of elements representing different aquifers and aquitards, for example) and within that 3D mesh you might have included 2D elements to represent the fractures. Those 2D elements must share nodes with the 3D elements for the MOOSE model to make sense. The 2D elements belong to a different set of subdomains, and those subdomains typically have different Material properties assigned to them (for example, high permeability and porosity). If you want to measure Darcy velocity within those lower-dimensional subdomains, then use this AuxKernel.

This AuxKernel calculates the x, y, or z component of the Darcy velocity $var element = document.getElementById("moose-equation-6dba05f4-6d8b-45de-8eff-051a59ab25ee");katex.render(" -\\frac{k\\,k_{\\mathrm{r,}\\beta}}{a\\mu_{\\beta}}(\\nabla P_{\\beta} - \\rho_{\\beta} \\mathbf{g})", element, {displayMode:true,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ for fluid phase $var element = document.getElementById("moose-equation-bb4cf7a0-96ab-43f4-af3e-fb53339bfbe9");katex.render("\\beta", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ , where $var element = document.getElementById("moose-equation-77300e34-8933-4651-925f-cfec679745b2");katex.render("\\nabla P_{\\beta}", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ and $var element = document.getElementById("moose-equation-7c5a0d48-d4db-4e9b-a29a-6decaf7894bb");katex.render("\\mathbf{g}", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ are projected onto the tangent direction of the lower-dimensional element. All parameters are defined in the nomenclature.

Notice that the denominator of this expression includes $var element = document.getElementById("moose-equation-5ca58fd5-3e50-4b67-8309-d9c47b39dbd4");katex.render("a", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ , which is the fracture aperture. If the user doesn't want to divide by $var element = document.getElementById("moose-equation-58de35c4-2590-4994-9032-7602bc40c2c5");katex.render("a", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ , the default value of $var element = document.getElementById("moose-equation-7b0e253d-4123-4484-80ac-ada8c6ff9acc");katex.render("a=1", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ should be used. However, it is likely that when using this AuxKernel the dimensions of permeability will be m $var element = document.getElementById("moose-equation-687e501e-e30d-4011-af2f-dc484ea01e45");katex.render("^{3}", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ , because of a pre-multiplication by the fracture aperture. The denominator includes $var element = document.getElementById("moose-equation-e2b7f00c-6d33-4112-b39d-eba91cda83c2");katex.render("a", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ so that the unconventional units of permeability may be accounted for if desired.

note

As this AuxKernel uses material properties, only elemental (Monomial) AuxVariables can be used. The AuxVariables must be defined on the lower-dimensional subdomain only.

warning

For the result to make sense, the permeability tensor, $var element = document.getElementById("moose-equation-56109f45-1334-4b2f-b95b-9d13b2c03ab9");katex.render("k", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ , must not rotate tangential vectors to non-tangential vectors. For instance, an isotropic permeability tensor is sensible.

Input Parameters

PorousFlowDictatorThe UserObject that holds the list of PorousFlow variable names
C++ Type:UserObjectName
Controllable:No
Description:The UserObject that holds the list of PorousFlow variable names
componentThe spatial component of the Darcy flux to return
C++ Type:MooseEnum
Options:x, y, z
Controllable:No
Description:The spatial component of the Darcy flux to return
gravityGravitational acceleration vector downwards (m/s^2)
C++ Type:libMesh::VectorValue<double>
Controllable:No
Description:Gravitational acceleration vector downwards (m/s^2)
variableThe name of the variable that this object applies to
C++ Type:AuxVariableName
Controllable:No
Description:The name of the variable that this object applies to

Required Parameters

aperture1.0Aperture of the fracture
Default:1.0
C++ Type:std::vector<VariableName>
Controllable:No
Description:Aperture of the fracture
blockThe list of blocks (ids or names) that this object will be applied
C++ Type:std::vector<SubdomainName>
Controllable:No
Description:The list of blocks (ids or names) that this object will be applied
boundaryThe list of boundaries (ids or names) from the mesh where this object applies
C++ Type:std::vector<BoundaryName>
Controllable:No
Description:The list of boundaries (ids or names) from the mesh where this object applies
check_boundary_restrictedTrueWhether to check for multiple element sides on the boundary in the case of a boundary restricted, element aux variable. Setting this to false will allow contribution to a single element's elemental value(s) from multiple boundary sides on the same element (example: when the restricted boundary exists on two or more sides of an element, such as at a corner of a mesh
Default:True
C++ Type:bool
Controllable:No
Description:Whether to check for multiple element sides on the boundary in the case of a boundary restricted, element aux variable. Setting this to false will allow contribution to a single element's elemental value(s) from multiple boundary sides on the same element (example: when the restricted boundary exists on two or more sides of an element, such as at a corner of a mesh
execute_onLINEAR TIMESTEP_ENDThe list of flag(s) indicating when this object should be executed, the available options include FORWARD, ADJOINT, HOMOGENEOUS_FORWARD, ADJOINT_TIMESTEP_BEGIN, ADJOINT_TIMESTEP_END, NONE, INITIAL, LINEAR, NONLINEAR, POSTCHECK, TIMESTEP_END, TIMESTEP_BEGIN, MULTIAPP_FIXED_POINT_END, MULTIAPP_FIXED_POINT_BEGIN, FINAL, CUSTOM, PRE_DISPLACE.
Default:LINEAR TIMESTEP_END
C++ Type:ExecFlagEnum
Options:FORWARD, ADJOINT, HOMOGENEOUS_FORWARD, ADJOINT_TIMESTEP_BEGIN, ADJOINT_TIMESTEP_END, NONE, INITIAL, LINEAR, NONLINEAR, POSTCHECK, TIMESTEP_END, TIMESTEP_BEGIN, MULTIAPP_FIXED_POINT_END, MULTIAPP_FIXED_POINT_BEGIN, FINAL, CUSTOM, PRE_DISPLACE
Controllable:No
Description:The list of flag(s) indicating when this object should be executed, the available options include FORWARD, ADJOINT, HOMOGENEOUS_FORWARD, ADJOINT_TIMESTEP_BEGIN, ADJOINT_TIMESTEP_END, NONE, INITIAL, LINEAR, NONLINEAR, POSTCHECK, TIMESTEP_END, TIMESTEP_BEGIN, MULTIAPP_FIXED_POINT_END, MULTIAPP_FIXED_POINT_BEGIN, FINAL, CUSTOM, PRE_DISPLACE.
fluid_phase0The index corresponding to the fluid phase
Default:0
C++ Type:unsigned int
Controllable:No
Description:The index corresponding to the 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
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
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

control_tagsAdds user-defined labels for accessing object parameters via control logic.
C++ Type:std::vector<std::string>
Controllable:No
Description:Adds user-defined labels for accessing object parameters via control logic.
enableTrueSet the enabled status of the MooseObject.
Default:True
C++ Type:bool
Controllable:Yes
Description:Set the enabled status of the MooseObject.
seed0The seed for the master random number generator
Default:0
C++ Type:unsigned int
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
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/examples/flow_through_fractured_media/coarse.i)
(modules/porous_flow/examples/flow_through_fractured_media/coarse_3D.i)
(modules/porous_flow/examples/flow_through_fractured_media/fine_transient.i)
(modules/porous_flow/test/tests/aux_kernels/darcy_velocity_lower_2D.i)
(modules/porous_flow/test/tests/aux_kernels/darcy_velocity_lower.i)
(modules/porous_flow/test/tests/aux_kernels/darcy_velocity_lower_except.i)

(modules/porous_flow/examples/flow_through_fractured_media/coarse.i)

# Flow and solute transport along a fracture embedded in a porous matrix
# The fracture is represented by lower dimensional elements
# fracture aperture = 6e-4m
# fracture porosity = 6e-4m = phi * a
# fracture permeability = 1.8e-11 which is based on k=3e-8 from a**2/12, and k*a = 3e-8*6e-4
# matrix porosity = 0.1
# matrix permeanility = 1e-20

[Mesh]
  type = FileMesh
  file = 'coarse.e'
  block_id = '1 2 3'
  block_name = 'fracture matrix1 matrix2'

  boundary_id = '1 2'
  boundary_name = 'bottom top'
[]

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

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

[AuxVariables]
  [velocity_x]
    family = MONOMIAL
    order = CONSTANT
    block = 'fracture'
  []
  [velocity_y]
    family = MONOMIAL
    order = CONSTANT
    block = 'fracture'
  []
[]

[AuxKernels]
  [velocity_x]
    type = PorousFlowDarcyVelocityComponentLowerDimensional
    variable = velocity_x
    component = x
    aperture = 6E-4
  []
  [velocity_y]
    type = PorousFlowDarcyVelocityComponentLowerDimensional
    variable = velocity_y
    component = y
    aperture = 6E-4
  []
[]

[ICs]
  [massfrac0]
    type = ConstantIC
    variable = massfrac0
    value = 0
  []
  [pp_matrix]
    type = ConstantIC
    variable = pp
    value = 1E6
  []
[]

[BCs]
  [top]
    type = DirichletBC
    value = 0
    variable = massfrac0
    boundary = top
  []
  [bottom]
    type = DirichletBC
    value = 1
    variable = massfrac0
    boundary = bottom
  []
  [ptop]
    type = DirichletBC
    variable = pp
    boundary =  top
    value = 1e6
  []
  [pbottom]
    type = DirichletBC
    variable = pp
    boundary = bottom
    value = 1.002e6
  []
[]

[Kernels]
  [mass0]
    type = PorousFlowMassTimeDerivative
    fluid_component = 1
    variable = pp
  []
  [adv0]
    type = PorousFlowAdvectiveFlux
    fluid_component = 1
    variable = pp
  []
  [diff0]
    type = PorousFlowDispersiveFlux
    fluid_component = 1
    variable = pp
    disp_trans = 0
    disp_long = 0
  []
  [mass1]
    type = PorousFlowMassTimeDerivative
    fluid_component = 0
    variable = massfrac0
  []
  [adv1]
    type = PorousFlowAdvectiveFlux
    fluid_component = 0
    variable = massfrac0
  []
  [diff1]
    type = PorousFlowDispersiveFlux
    fluid_component = 0
    variable = massfrac0
    disp_trans = 0
    disp_long = 0
  []
[]

[UserObjects]
  [dictator]
    type = PorousFlowDictator
    porous_flow_vars = 'pp massfrac0'
    number_fluid_phases = 1
    number_fluid_components = 2
  []
[]

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

[Materials]
  [temperature]
    type = PorousFlowTemperature
  []
  [ppss]
    type = PorousFlow1PhaseFullySaturated
    porepressure = pp
  []
  [massfrac]
    type = PorousFlowMassFraction
    mass_fraction_vars = massfrac0
  []
  [simple_fluid]
    type = PorousFlowSingleComponentFluid
    fp = simple_fluid
    phase = 0
  []
  [poro_fracture]
    type = PorousFlowPorosityConst
    porosity = 6e-4   # = a * phif
    block = 'fracture'
  []
  [poro_matrix]
    type = PorousFlowPorosityConst
    porosity = 0.1
    block = 'matrix1 matrix2'
  []
  [diff1]
    type = PorousFlowDiffusivityConst
    diffusion_coeff = '1e-9 1e-9'
    tortuosity = 1.0
    block = 'fracture'
  []
  [diff2]
    type = PorousFlowDiffusivityConst
    diffusion_coeff = '1e-9 1e-9'
    tortuosity = 0.1
    block = 'matrix1 matrix2'
  []
  [permeability_fracture]
    type = PorousFlowPermeabilityConst
    permeability = '1.8e-11 0 0 0 1.8e-11 0 0 0 1.8e-11'   # 1.8e-11 = a * kf
    block = 'fracture'
  []
  [permeability_matrix]
    type = PorousFlowPermeabilityConst
    permeability = '1e-20 0 0 0 1e-20 0 0 0 1e-20'
    block = 'matrix1 matrix2'
  []
  [relp]
    type = PorousFlowRelativePermeabilityConst
    phase = 0
  []
[]

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

[Executioner]
  type = Transient
  solve_type = NEWTON
  end_time = 10
  dt = 1

# controls for nonlinear iterations
  nl_max_its = 15
  nl_rel_tol = 1e-14
  nl_abs_tol = 1e-12

[]

[VectorPostprocessors]
  [xmass]
    type = LineValueSampler
    start_point = '-0.5 0 0'
    end_point = '0.5 0 0'
    sort_by = x
    num_points = 41
    variable = massfrac0
    outputs = csv
  []
[]

[Outputs]
  [csv]
    type = CSV
    execute_on = 'final'
  []
[]

(modules/porous_flow/examples/flow_through_fractured_media/coarse_3D.i)

# Flow and solute transport along 2 2D eliptical fractures embedded in a 3D porous matrix
# the model domain has dimensions 1 x 1 x 0.3m and the two fracture have r1 = 0.45 and r2 = 0.2
# The fractures intersect each other and the domain boundaries on two opposite sides
# fracture aperture = 6e-4m
# fracture porosity = 6e-4m
# fracture permeability = 1.8e-11 which is based in k=3e-8 from a**2/12, and k*a = 3e-8*6e-4;
# matrix porosity = 0.1;
# matrix permeanility = 1e-20;

[Mesh]
  type = FileMesh
  file = coarse_3D.e
  block_id = '1 2 3'
  block_name = 'matrix f1 f2'

  boundary_id = '1 2 3 4'
  boundary_name = 'rf2 lf1 right_matrix left_matrix'
[]

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

[Variables]
  [pp]
  []
  [tracer]
  []
[]

[AuxVariables]
  [velocity_x]
    family = MONOMIAL
    order = CONSTANT
    block = 'f1 f2'
  []
  [velocity_y]
    family = MONOMIAL
    order = CONSTANT
    block = 'f1 f2'
  []
  [velocity_z]
    family = MONOMIAL
    order = CONSTANT
    block = 'f1 f2'
  []
[]

[AuxKernels]
  [velocity_x]
    type = PorousFlowDarcyVelocityComponentLowerDimensional
    variable = velocity_x
    component = x
    aperture = 6E-4
  []
  [velocity_y]
    type = PorousFlowDarcyVelocityComponentLowerDimensional
    variable = velocity_y
    component = y
    aperture = 6E-4
  []
  [velocity_z]
    type = PorousFlowDarcyVelocityComponentLowerDimensional
    variable = velocity_z
    component = z
    aperture = 6E-4
  []
[]

[ICs]
  [pp]
    type = ConstantIC
    variable = pp
    value = 1e6
  []
  [tracer]
    type = ConstantIC
    variable = tracer
    value = 0
  []
[]

[BCs]
  [top]
    type = DirichletBC
    value = 0
    variable = tracer
    boundary = rf2
  []
  [bottom]
    type = DirichletBC
    value = 1
    variable = tracer
    boundary = lf1
  []
  [ptop]
    type = DirichletBC
    variable = pp
    boundary =  rf2
    value = 1e6
  []
  [pbottom]
    type = DirichletBC
    variable = pp
    boundary = lf1
    value = 1.02e6
  []
[]

[Kernels]
  [mass0]
    type = PorousFlowMassTimeDerivative
    fluid_component = 0
    variable = pp
  []
  [adv0]
    type = PorousFlowAdvectiveFlux
    fluid_component = 0
    variable = pp
  []
  [diff0]
    type = PorousFlowDispersiveFlux
    fluid_component = 0
    variable = pp
    disp_trans = 0
    disp_long = 0
  []
  [mass1]
    type = PorousFlowMassTimeDerivative
    fluid_component = 1
    variable = tracer
  []
  [adv1]
    type = PorousFlowAdvectiveFlux
    fluid_component = 1
    variable = tracer
  []
  [diff1]
    type = PorousFlowDispersiveFlux
    fluid_component = 1
    variable = tracer
    disp_trans = 0
    disp_long = 0
  []
[]

[UserObjects]
  [dictator]
    type = PorousFlowDictator
    porous_flow_vars = 'pp tracer'
    number_fluid_phases = 1
    number_fluid_components = 2
  []
[]

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

[Materials]
  [temperature]
    type = PorousFlowTemperature
  []
  [ppss]
    type = PorousFlow1PhaseFullySaturated
    porepressure = pp
  []
  [massfrac]
    type = PorousFlowMassFraction
    mass_fraction_vars = 'tracer'
  []
  [simple_fluid]
    type = PorousFlowSingleComponentFluid
    fp = simple_fluid
    phase = 0
  []
  [poro1]
    type = PorousFlowPorosityConst
    porosity = 6e-4   # = a * phif
    block = 'f1 f2'
  []
  [diff1]
    type = PorousFlowDiffusivityConst
    diffusion_coeff = '1.e-9 1.e-9'
    tortuosity = 1.0
    block = 'f1 f2'
  []
  [poro2]
    type = PorousFlowPorosityConst
    porosity = 0.1
    block = 'matrix'
  []
  [diff2]
    type = PorousFlowDiffusivityConst
    diffusion_coeff = '1.e-9 1.e-9'
    tortuosity = 0.1
    block = 'matrix'
  []
  [relp]
    type = PorousFlowRelativePermeabilityConst
    phase = 0
  []
  [permeability1]
    type = PorousFlowPermeabilityConst
    permeability = '1.8e-11 0 0 0 1.8e-11 0 0 0 1.8e-11'   # 1.8e-11 = a * kf
    block = 'f1 f2'
  []
  [permeability2]
    type = PorousFlowPermeabilityConst
    permeability = '1e-20 0 0 0 1e-20 0 0 0 1e-20'
    block = 'matrix'
  []
[]

[Preconditioning]
  active = basic
  [mumps_is_best_for_parallel_jobs]
    type = SMP
    full = true
    petsc_options_iname = '-pc_type -pc_factor_mat_solver_package'
    petsc_options_value = ' lu       mumps'
  []
  [basic]
    type = SMP
    full = true
    petsc_options_iname = '-ksp_type -pc_type -sub_pc_type -sub_pc_factor_shift_type -pc_asm_overlap'
    petsc_options_value = 'gmres      asm      lu           NONZERO                   2             '
  []
[]

[Executioner]
  type = Transient
  solve_type = NEWTON
  end_time = 20
  dt = 1
[]

[VectorPostprocessors]
  [xmass]
    type = LineValueSampler
    start_point = '-0.5 0 0'
    end_point = '0.5 0 0'
    sort_by = x
    num_points = 41
    variable = tracer
    outputs = csv
  []
[]

[Outputs]
  [csv]
    type = CSV
    execute_on = 'final'
  []
[]

(modules/porous_flow/examples/flow_through_fractured_media/fine_transient.i)

# Using a mixed-dimensional mesh
# Transient flow and solute transport along a fracture in a porous matrix
# advective dominated flow in the fracture and diffusion into the porous matrix
#
# Note that fine_steady.i must be run to initialise the porepressure properly

[Mesh]
  file = 'gold/fine_steady_out.e'
[]

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

[Variables]
  [pp]
    initial_from_file_var = pp
    initial_from_file_timestep = 1
  []
  [massfrac0]
  []
[]

[AuxVariables]
  [velocity_x]
    family = MONOMIAL
    order = CONSTANT
    block = fracture
  []
  [velocity_y]
    family = MONOMIAL
    order = CONSTANT
    block = fracture
  []
[]

[AuxKernels]
  [velocity_x]
    type = PorousFlowDarcyVelocityComponentLowerDimensional
    variable = velocity_x
    component = x
    aperture = 6E-4
  []
  [velocity_y]
    type = PorousFlowDarcyVelocityComponentLowerDimensional
    variable = velocity_y
    component = y
    aperture = 6E-4
  []
[]

[Problem]
  # massfrac0 has an initial condition despite the restart
  allow_initial_conditions_with_restart = true
[]

[ICs]
  [massfrac0]
    type = ConstantIC
    variable = massfrac0
    value = 0
  []
[]

[BCs]
  [top]
    type = DirichletBC
    value = 0
    variable = massfrac0
    boundary = top
  []
  [bottom]
    type = DirichletBC
    value = 1
    variable = massfrac0
    boundary = bottom
  []
  [ptop]
    type = DirichletBC
    variable = pp
    boundary = top
    value = 1e6
  []
  [pbottom]
    type = DirichletBC
    variable = pp
    boundary = bottom
    value = 1.002e6
  []
[]

[Kernels]
  [mass0]
    type = PorousFlowMassTimeDerivative
    fluid_component = 0
    variable = pp
  []
  [adv0]
    type = PorousFlowAdvectiveFlux
    fluid_component = 0
    variable = pp
  []
  [diff0]
    type = PorousFlowDispersiveFlux
    fluid_component = 0
    variable = pp
    disp_trans = 0
    disp_long = 0
  []
  [mass1]
    type = PorousFlowMassTimeDerivative
    fluid_component = 1
    variable = massfrac0
  []
  [adv1]
    type = PorousFlowAdvectiveFlux
    fluid_component = 1
    variable = massfrac0
  []
  [diff1]
    type = PorousFlowDispersiveFlux
    fluid_component = 1
    variable = massfrac0
    disp_trans = 0
    disp_long = 0
  []
[]

[UserObjects]
  [dictator]
    type = PorousFlowDictator
    porous_flow_vars = 'pp massfrac0'
    number_fluid_phases = 1
    number_fluid_components = 2
  []
[]

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

[Materials]
  [temperature]
    type = PorousFlowTemperature
  []
  [ppss]
    type = PorousFlow1PhaseFullySaturated
    porepressure = pp
  []
  [massfrac]
    type = PorousFlowMassFraction
    mass_fraction_vars = massfrac0
  []
  [simple_fluid]
    type = PorousFlowSingleComponentFluid
    fp = simple_fluid
    phase = 0
  []
  [poro_fracture]
    type = PorousFlowPorosityConst
    porosity = 6e-4 # = a * phif
    block = 'fracture'
  []
  [poro_matrix]
    type = PorousFlowPorosityConst
    porosity = 0.1
    block = 'matrix1 matrix2'
  []
  [diff1]
    type = PorousFlowDiffusivityConst
    diffusion_coeff = '1e-9 1e-9'
    tortuosity = 1.0
    block = 'fracture'
  []
  [diff2]
    type = PorousFlowDiffusivityConst
    diffusion_coeff = '1e-9 1e-9'
    tortuosity = 0.1
    block = 'matrix1 matrix2'
  []
  [relp]
    type = PorousFlowRelativePermeabilityConst
    phase = 0
  []
  [permeability_fracture]
    type = PorousFlowPermeabilityConst
    permeability = '1.8e-11 0 0 0 1.8e-11 0 0 0 1.8e-11' # kf=3e-8, a=6e-4m.  1.8e-11 = kf * a
    block = 'fracture'
  []
  [permeability_matrix]
    type = PorousFlowPermeabilityConst
    permeability = '1e-20 0 0 0 1e-20 0 0 0 1e-20'
    block = 'matrix1 matrix2'
  []
[]

[Functions]
  [dt_controller]
    type = PiecewiseConstant
    x = '0    30   40 100 200 83200'
    y = '0.01 0.1  1  10  100 32'
  []
[]

[Preconditioning]
  active = basic
  [mumps_is_best_for_parallel_jobs]
    type = SMP
    full = true
    petsc_options_iname = '-pc_type -pc_factor_mat_solver_package'
    petsc_options_value = ' lu       mumps'
  []
  [basic]
    type = SMP
    full = true
    petsc_options_iname = '-ksp_type -pc_type -sub_pc_type -sub_pc_factor_shift_type -pc_asm_overlap'
    petsc_options_value = 'gmres      asm      lu           NONZERO                   2             '
  []
[]

[Executioner]
  type = Transient
  solve_type = NEWTON
  end_time = 86400

  [TimeStepper]
    type = FunctionDT
    function = dt_controller
  []

  # controls for nonlinear iterations
  nl_max_its = 15
  nl_rel_tol = 1e-14
  nl_abs_tol = 1e-9
[]

[VectorPostprocessors]
  [xmass]
    type = LineValueSampler
    start_point = '0.4 0 0'
    end_point = '0.5 0 0'
    sort_by = x
    num_points = 167
    variable = massfrac0
  []
[]

[Outputs]
  perf_graph = true
  console = true
  csv = true
  exodus = true
[]

(modules/porous_flow/test/tests/aux_kernels/darcy_velocity_lower_2D.i)

# checking that the PorousFlowDarcyVelocityComponentLowerDimensional AuxKernel works as expected in 1D+2D situation
# for the fully-saturated case (relative-permeability = 1)
# The 1_frac_in_2D_example.e has size 0.3x0.2x0, and a fracture running through its
# centre, with normal = (0, 1, 0)
# Porepressure is initialised to grad(P) = (1, 2, 0)
# Fluid_density = 2
# viscosity = 10
# relative_permeability = 1
# permeability = (5, 5, 5)  (in the bulk, measured in m^2)
# permeability = (10, 10, 10)   (in the fracture, measured in m^3)
# aperture = 0.01
# gravity = (1, 0.5, 0)
# So Darcy velocity in the bulk = (0.5, -0.5, 0)
# in the fracture grad(P) = (1, 0, 0)
# In the fracture the projected gravity vector is
# tangential_gravity = (1, 0, 0)
# So the Darcy velocity in the fracture = (100, 0, 0)

[Mesh]
  type = FileMesh
  file = 1_frac_in_2D_example.e
[]

[GlobalParams]
  PorousFlowDictator = dictator
  gravity = '1 0.5 0'
[]

[Variables]
  [pp]
  []
[]

[ICs]
  [pinit]
    type = FunctionIC
    function = 'x+2*y'
    variable = pp
  []
[]

[Kernels]
  [dummy]
    type = TimeDerivative
    variable = pp
  []
[]

[AuxVariables]
  [bulk_vel_x]
    order = CONSTANT
    family = MONOMIAL
    block = '2 3'
  []
  [bulk_vel_y]
    order = CONSTANT
    family = MONOMIAL
    block = '2 3'
  []
  [bulk_vel_z]
    order = CONSTANT
    family = MONOMIAL
    block = '2 3'
  []
  [fracture_vel_x]
    order = CONSTANT
    family = MONOMIAL
    block = 1
  []
  [fracture_vel_y]
    order = CONSTANT
    family = MONOMIAL
    block = 1
  []
  [fracture_vel_z]
    order = CONSTANT
    family = MONOMIAL
    block = 1
  []
[]

[AuxKernels]
  [bulk_vel_x]
    type = PorousFlowDarcyVelocityComponent
    variable = bulk_vel_x
    component = x
    fluid_phase = 0
  []
  [bulk_vel_y]
    type = PorousFlowDarcyVelocityComponent
    variable = bulk_vel_y
    component = y
    fluid_phase = 0
  []
  [bulk_vel_z]
    type = PorousFlowDarcyVelocityComponent
    variable = bulk_vel_z
    component = z
    fluid_phase = 0
  []
  [fracture_vel_x]
    type = PorousFlowDarcyVelocityComponentLowerDimensional
    variable = fracture_vel_x
    component = x
    fluid_phase = 0
    aperture = 0.01
  []
  [fracture_vel_y]
    type = PorousFlowDarcyVelocityComponentLowerDimensional
    variable = fracture_vel_y
    component = y
    fluid_phase = 0
    aperture = 0.01
  []
  [fracture_vel_z]
    type = PorousFlowDarcyVelocityComponentLowerDimensional
    variable = fracture_vel_z
    component = z
    fluid_phase = 0
    aperture = 0.01
  []
[]

[UserObjects]
  [dictator]
    type = PorousFlowDictator
    porous_flow_vars = 'pp'
    number_fluid_phases = 1
    number_fluid_components = 1
  []
  [pc]
    type = PorousFlowCapillaryPressureConst
    pc = 0
  []
[]

[FluidProperties]
  [simple_fluid]
    type = SimpleFluidProperties
    bulk_modulus = 1E16
    viscosity = 10
    density0 = 2
    thermal_expansion = 0
  []
[]

[Postprocessors]
  [bulk_vel_x]
    type = PointValue
    variable = bulk_vel_x
    point = '0 -0.05 0'
  []
  [bulk_vel_y]
    type = PointValue
    variable = bulk_vel_y
    point = '0 -0.05 0'
  []
  [bulk_vel_z]
    type = PointValue
    variable = bulk_vel_z
    point = '0 -0.05 0'
  []
  [fracture_vel_x]
    type = PointValue
    point = '0 0 0'
    variable = fracture_vel_x
  []
  [fracture_vel_y]
    type = PointValue
    point = '0 0 0'
    variable = fracture_vel_y
  []
  [fracture_vel_z]
    type = PointValue
    point = '0 0 0'
    variable = fracture_vel_z
  []
[]

[Materials]
  [temperature]
    type = PorousFlowTemperature
  []
  [ppss]
    type = PorousFlow1PhaseP
    porepressure = pp
    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'
    block = '2 3'
  []
  [permeability_fracture]
    type = PorousFlowPermeabilityConst
    permeability = '10 0 0 0 10 0 0 0 10'
    block = 1
  []
  [relperm]
    type = PorousFlowRelativePermeabilityCorey
    n = 2
    phase = 0
  []
[]

[Executioner]
  type = Transient
  dt = 1
  end_time = 1
[]

[Outputs]
  csv = true
[]

(modules/porous_flow/test/tests/aux_kernels/darcy_velocity_lower.i)

# checking that the PorousFlowDarcyVelocityComponentLowerDimensional AuxKernel works as expected
# for the fully-saturated case (relative-permeability = 1)
# The fractured_block.e has size = 10x10x10, and a fracture running through its
# centre, with normal = (0, -sin(20deg), cos(20deg))
# Porepressure is initialised to grad(P) = (0, 0, 1)
# Fluid_density = 2
# viscosity = 10
# relative_permeability = 1
# permeability = (5, 5, 5)  (in the bulk)
# permeability = (10, 10, 10)   (in the fracture)
# aperture = 1
# gravity = (1, 0.5, 0.2)
# So Darcy velocity in the bulk = (1, 0.5, -0.3)
# in the fracture grad(P) = (0, 0.3213938, 0.11697778)
# In the fracture the projected gravity vector is
# tangential_gravity = (1, 0.5057899, 0.18409245)
# So the Darcy velocity in the fracture = (2, 0.690186, 0.251207)

[Mesh]
  type = FileMesh
  file = fractured_block.e
[]

[GlobalParams]
  PorousFlowDictator = dictator
  gravity = '1 0.5 0.2'
[]

[Variables]
  [pp]
  []
[]

[ICs]
  [pinit]
    type = FunctionIC
    function = z
    variable = pp
  []
[]

[Kernels]
  [dummy]
    type = TimeDerivative
    variable = pp
  []
[]

[AuxVariables]
  [bulk_vel_x]
    order = CONSTANT
    family = MONOMIAL
  []
  [bulk_vel_y]
    order = CONSTANT
    family = MONOMIAL
  []
  [bulk_vel_z]
    order = CONSTANT
    family = MONOMIAL
  []
  [fracture_vel_x]
    order = CONSTANT
    family = MONOMIAL
    block = 3
  []
  [fracture_vel_y]
    order = CONSTANT
    family = MONOMIAL
    block = 3
  []
  [fracture_vel_z]
    order = CONSTANT
    family = MONOMIAL
    block = 3
  []
[]

[AuxKernels]
  [bulk_vel_x]
    type = PorousFlowDarcyVelocityComponent
    variable = bulk_vel_x
    component = x
    fluid_phase = 0
  []
  [bulk_vel_y]
    type = PorousFlowDarcyVelocityComponent
    variable = bulk_vel_y
    component = y
    fluid_phase = 0
  []
  [bulk_vel_z]
    type = PorousFlowDarcyVelocityComponent
    variable = bulk_vel_z
    component = z
    fluid_phase = 0
  []
  [fracture_vel_x]
    type = PorousFlowDarcyVelocityComponentLowerDimensional
    variable = fracture_vel_x
    component = x
    fluid_phase = 0
  []
  [fracture_vel_y]
    type = PorousFlowDarcyVelocityComponentLowerDimensional
    variable = fracture_vel_y
    component = y
    fluid_phase = 0
  []
  [fracture_vel_z]
    type = PorousFlowDarcyVelocityComponentLowerDimensional
    variable = fracture_vel_z
    component = z
    fluid_phase = 0
 []
[]

[UserObjects]
  [dictator]
    type = PorousFlowDictator
    porous_flow_vars = 'pp'
    number_fluid_phases = 1
    number_fluid_components = 1
  []
  [pc]
    type = PorousFlowCapillaryPressureConst
    pc = 0
  []
[]

[FluidProperties]
  [simple_fluid]
    type = SimpleFluidProperties
    bulk_modulus = 1E16
    viscosity = 10
    density0 = 2
    thermal_expansion = 0
  []
[]

[Postprocessors]
  [bulk_vel_x]
    type = ElementAverageValue
    block = 1
    variable = bulk_vel_x
  []
  [bulk_vel_y]
    type = ElementAverageValue
    block = 1
    variable = bulk_vel_y
  []
  [bulk_vel_z]
    type = ElementAverageValue
    block = 1
    variable = bulk_vel_z
  []
  [fracture_vel_x]
    type = ElementAverageValue
    block = 3
    variable = fracture_vel_x
  []
  [fracture_vel_y]
    type = ElementAverageValue
    block = 3
    variable = fracture_vel_y
  []
  [fracture_vel_z]
    type = ElementAverageValue
    block = 3
    variable = fracture_vel_z
  []
[]

[Materials]
  [temperature]
    type = PorousFlowTemperature
  []
  [ppss]
    type = PorousFlow1PhaseP
    porepressure = pp
    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'
    block = '1 2'
  []
  [permeability_fracture]
    type = PorousFlowPermeabilityConst
    permeability = '10 0 0 0 10 0 0 0 10'
    block = 3
  []
  [relperm]
    type = PorousFlowRelativePermeabilityCorey
    n = 2
    phase = 0
  []
[]

[Executioner]
  type = Transient
  dt = 1
  end_time = 1
[]

[Outputs]
  csv = true
[]

(modules/porous_flow/test/tests/aux_kernels/darcy_velocity_lower_except.i)

# Exception testing for PorousFlowDarcyVelocityComponentLowerDimensional
# Checking that an error is produced if the AuxVariable is not defined only on
# lower-dimensional elements
[Mesh]
  type = FileMesh
  file = fractured_block.e
[]

[GlobalParams]
  PorousFlowDictator = dictator
  gravity = '1 0.5 0.2'
[]

[Variables]
  [pp]
  []
[]

[Kernels]
  [dummy]
    type = TimeDerivative
    variable = pp
  []
[]

[AuxVariables]
  [fracture_vel_x]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[AuxKernels]
  [fracture_vel_x]
    type = PorousFlowDarcyVelocityComponentLowerDimensional
    variable = fracture_vel_x
    component = x
    fluid_phase = 0
  []
[]

[UserObjects]
  [dictator]
    type = PorousFlowDictator
    porous_flow_vars = 'pp'
    number_fluid_phases = 1
    number_fluid_components = 1
  []
  [pc]
    type = PorousFlowCapillaryPressureConst
    pc = 0
  []
[]

[FluidProperties]
  [simple_fluid]
    type = SimpleFluidProperties
    bulk_modulus = 1E16
    viscosity = 10
    density0 = 2
    thermal_expansion = 0
  []
[]

[Materials]
  [temperature]
    type = PorousFlowTemperature
  []
  [ppss]
    type = PorousFlow1PhaseP
    porepressure = pp
    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 = 2
    phase = 0
  []
[]

[Executioner]
  type = Transient
  dt = 1
  end_time = 1
[]

Input Parameters
Input Files