WCNSFV2PSlipVelocityFunctorMaterial

This material computes the slip velocity between a dispersed phase and a mixture phase. The slip velocity is modeled as follows:

$var element = document.getElementById("moose-equation-9bb0585e-618a-43ef-8a61-b65ba3f67dc9");katex.render(" \\bm{v}_{slip,d} = \\frac{\\tau_d}{f_{drag}} \\frac{\\rho_d - \\rho_m}{\\rho_d} \\bm{a} \\,,", element, {displayMode:true,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$

where:

$var element = document.getElementById("moose-equation-ecd795f2-6351-4657-9264-31d2df496bc0");katex.render("\\tau_d", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ is the particle relaxation time,
$var element = document.getElementById("moose-equation-b79e1797-7d15-4a52-b0d8-95ea4f9a1a3a");katex.render("f_{drag}", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ is the linear drag coefficient function,
$var element = document.getElementById("moose-equation-b6ca00fe-ed66-4433-9552-0be86e68af42");katex.render("\\rho_d", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ is the density of the dispersed phase,
$var element = document.getElementById("moose-equation-4757751a-c4eb-424c-9367-b6fa8a7b3b82");katex.render("\\rho_m", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ is the density of the mixture,
$var element = document.getElementById("moose-equation-5f724110-db8e-4a6d-b3e4-a56310f2b759");katex.render("\\bm{a}", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ is the acceleration vector.

The particle relaxation time is modeled as follows Bilicki and Kestin (1990):

$var element = document.getElementById("moose-equation-1c5572f0-0791-44e2-9ac1-bf28d615e01d");katex.render(" \\tau_d = \\frac{\\rho_d d_d^2}{18 \\mu_m} \\,,", element, {displayMode:true,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$

where:

$var element = document.getElementById("moose-equation-4ab53d7a-b8ab-4115-a6ea-dec2d8168a2c");katex.render("d_d", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ is the particle diameter,
$var element = document.getElementById("moose-equation-c8910251-d0ff-4efb-bc00-249ec8767c11");katex.render("\\mu_m", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ is the mixture dynamic viscosity.

The acceleration vector is the particle acceleration vector:

$var element = document.getElementById("moose-equation-1841ef2a-e064-4d8e-9dd1-46deada678bf");katex.render(" \\bm{a} = \\bm{g} + \\frac{\\bm{f}}{\\rho_m} - \\bm{u}_m \\cdot \\nabla \\bm{u}_m - \\frac{\\partial \\bm{u}_m}{dt} \\,,", element, {displayMode:true,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$

where:

$var element = document.getElementById("moose-equation-67fb6c77-300c-4ced-96f8-1064afc4ec4e");katex.render("\\bm{g}", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ is the acceleration of gravity,
$var element = document.getElementById("moose-equation-cb3b5dcb-da43-4b99-9170-a71f6841400f");katex.render("\\bm{f}", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ is the volumetric force,
$var element = document.getElementById("moose-equation-35b69d2c-8854-49d9-a412-72108d50eca3");katex.render("\\bm{u}_m", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ is the mixture velocity.

Input Parameters

momentum_componentThe component of the momentum equation that this kernel applies to.
C++ Type:MooseEnum
Options:x, y, z
Controllable:No
Description:The component of the momentum equation that this kernel applies to.
muMixture Density. A functor is any of the following: a variable, a functor material property, a function, a post-processor, or a number.
C++ Type:MooseFunctorName
Controllable:No
Description:Mixture Density. A functor is any of the following: a variable, a functor material property, a function, a post-processor, or a number.
rhoContinuous phase density. A functor is any of the following: a variable, a functor material property, a function, a post-processor, or a number.
C++ Type:MooseFunctorName
Controllable:No
Description:Continuous phase density. A functor is any of the following: a variable, a functor material property, a function, a post-processor, or a number.
rho_dDispersed phase density. A functor is any of the following: a variable, a functor material property, a function, a post-processor, or a number.
C++ Type:MooseFunctorName
Controllable:No
Description:Dispersed phase density. A functor is any of the following: a variable, a functor material property, a function, a post-processor, or a number.
slip_velocity_namethe name of the slip velocity. A functor is any of the following: a variable, a functor material property, a function, a post-processor, or a number.
C++ Type:MooseFunctorName
Controllable:No
Description:the name of the slip velocity. A functor is any of the following: a variable, a functor material property, a function, a post-processor, or a number.
uThe velocity in the x direction.
C++ Type:std::vector<VariableName>
Controllable:No
Description:The velocity in the x direction.

Required Parameters

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
constant_onNONEWhen ELEMENT, MOOSE will only call computeQpProperties() for the 0th quadrature point, and then copy that value to the other qps.When SUBDOMAIN, MOOSE will only call computeQpProperties() for the 0th quadrature point, and then copy that value to the other qps. Evaluations on element qps will be skipped
Default:NONE
C++ Type:MooseEnum
Options:NONE, ELEMENT, SUBDOMAIN
Controllable:No
Description:When ELEMENT, MOOSE will only call computeQpProperties() for the 0th quadrature point, and then copy that value to the other qps.When SUBDOMAIN, MOOSE will only call computeQpProperties() for the 0th quadrature point, and then copy that value to the other qps. Evaluations on element qps will be skipped
execute_onALWAYSThe 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, TIMESTEP_END, TIMESTEP_BEGIN, MULTIAPP_FIXED_POINT_END, MULTIAPP_FIXED_POINT_BEGIN, FINAL, CUSTOM.
Default:ALWAYS
C++ Type:ExecFlagEnum
Options:FORWARD, ADJOINT, HOMOGENEOUS_FORWARD, ADJOINT_TIMESTEP_BEGIN, ADJOINT_TIMESTEP_END, NONE, INITIAL, LINEAR, NONLINEAR, TIMESTEP_END, TIMESTEP_BEGIN, MULTIAPP_FIXED_POINT_END, MULTIAPP_FIXED_POINT_BEGIN, FINAL, CUSTOM, ALWAYS
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, TIMESTEP_END, TIMESTEP_BEGIN, MULTIAPP_FIXED_POINT_END, MULTIAPP_FIXED_POINT_BEGIN, FINAL, CUSTOM.
fd0Fraction dispersed phase. A functor is any of the following: a variable, a functor material property, a function, a post-processor, or a number.
Default:0
C++ Type:MooseFunctorName
Controllable:No
Description:Fraction dispersed phase. A functor is any of the following: a variable, a functor material property, a function, a post-processor, or a number.
force_direction1 0 0Gravitational acceleration vector
Default:1 0 0
C++ Type:libMesh::VectorValue<double>
Controllable:No
Description:Gravitational acceleration vector
force_function0A function that describes the body force
Default:0
C++ Type:FunctionName
Controllable:No
Description:A function that describes the body force
force_postprocessor0A postprocessor whose value is multiplied by the body force
Default:0
C++ Type:PostprocessorName
Controllable:No
Description:A postprocessor whose value is multiplied by the body force
force_value0Coefficient to multiply by the body force term
Default:0
C++ Type:double
Controllable:No
Description:Coefficient to multiply by the body force term
ghost_layers3The number of layers of elements to ghost. With Rhie-Chow and the velocity gradient calculation below, we need 3
Default:3
C++ Type:unsigned short
Controllable:No
Description:The number of layers of elements to ghost. With Rhie-Chow and the velocity gradient calculation below, we need 3
gravity0 0 0Gravity acceleration vector
Default:0 0 0
C++ Type:libMesh::VectorValue<double>
Controllable:No
Description:Gravity acceleration vector
linear_coef_name0.44Linear friction coefficient name as a material property. A functor is any of the following: a variable, a functor material property, a function, a post-processor, or a number.
Default:0.44
C++ Type:MooseFunctorName
Controllable:No
Description:Linear friction coefficient name as a material property. A functor is any of the following: a variable, a functor material property, a function, a post-processor, or a number.
particle_diameter1Diameter of particles in the dispersed phase. A functor is any of the following: a variable, a functor material property, a function, a post-processor, or a number.
Default:1
C++ Type:MooseFunctorName
Controllable:No
Description:Diameter of particles in the dispersed phase. A functor is any of the following: a variable, a functor material property, a function, a post-processor, or a number.
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.
vThe velocity in the y direction.
C++ Type:std::vector<VariableName>
Controllable:No
Description:The velocity in the y direction.
wThe velocity in the z direction.
C++ Type:std::vector<VariableName>
Controllable:No
Description:The velocity in the z direction.

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.
implicitTrueDetermines whether this object is calculated using an implicit or explicit form
Default:True
C++ Type:bool
Controllable:No
Description:Determines whether this object is calculated using an implicit or explicit form
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

Advanced Parameters

output_propertiesList of material properties, from this material, to output (outputs must also be defined to an output type)
C++ Type:std::vector<std::string>
Controllable:No
Description:List of material properties, from this material, to output (outputs must also be defined to an output type)
outputsnone Vector of output names where you would like to restrict the output of variables(s) associated with this object
Default:none
C++ Type:std::vector<OutputName>
Controllable:No
Description:Vector of output names where you would like to restrict the output of variables(s) associated with this object

Outputs Parameters

Input Files

(modules/navier_stokes/test/tests/finite_volume/two_phase/mixture_model/rayleigh-bernard-two-phase.i)
(modules/navier_stokes/test/tests/finite_volume/two_phase/mixture_model/channel-drift-flux.i)
(modules/navier_stokes/test/tests/finite_volume/two_phase/mixture_model/channel-advection-slip.i)
(modules/navier_stokes/test/tests/finite_volume/two_phase/mixture_model/channel-drift-flux-transient.i)
(modules/navier_stokes/test/tests/finite_volume/two_phase/mixture_model/lid-driven-two-phase.i)

References

Zbigniew Bilicki and Joseph Kestin. Physical aspects of the relaxation model in two-phase flow. Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences, 428(1875):379–397, 1990.

@article{bilicki1990dragmodel,
    author = "Bilicki, Zbigniew and Kestin, Joseph",
    title = "Physical aspects of the relaxation model in two-phase flow",
    journal = "Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences",
    volume = "428",
    number = "1875",
    pages = "379--397",
    year = "1990",
    publisher = "The Royal Society London"
}

(modules/navier_stokes/test/tests/finite_volume/two_phase/mixture_model/rayleigh-bernard-two-phase.i)

mu = 1.0
rho = 1e3
mu_d = 0.3
rho_d = 1.0
dp = 0.01
U_lid = 0.0
g = -9.81

[GlobalParams]
  velocity_interp_method = 'rc'
  advected_interp_method = 'upwind'
  rhie_chow_user_object = 'rc'
[]

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 2
    xmin = 0
    xmax = .1
    ymin = 0
    ymax = .1
    nx = 11
    ny = 11
  []
[]

[Variables]
  [vel_x]
    type = INSFVVelocityVariable
  []
  [vel_y]
    type = INSFVVelocityVariable
  []
  [pressure]
    type = INSFVPressureVariable
  []
  [phase_2]
    type = INSFVScalarFieldVariable
  []
[]

[UserObjects]
  [rc]
    type = INSFVRhieChowInterpolator
    u = vel_x
    v = vel_y
    pressure = pressure
  []
  [pin_pressure]
    type = NSPressurePin
    variable = pressure
    pin_type = point-value
    point = '0 0 0'
  []
[]

[FVKernels]
  [mass]
    type = INSFVMassAdvection
    variable = pressure
    rho = 'rho_mixture'
  []

  [u_time]
    type = INSFVMomentumTimeDerivative
    variable = vel_x
    rho = 'rho_mixture'
    momentum_component = 'x'
  []
  [u_advection]
    type = INSFVMomentumAdvection
    variable = vel_x
    rho = 'rho_mixture'
    momentum_component = 'x'
  []
  [u_viscosity]
    type = INSFVMomentumDiffusion
    variable = vel_x
    mu = 'mu_mixture'
    momentum_component = 'x'
  []
  [u_pressure]
    type = INSFVMomentumPressure
    variable = vel_x
    momentum_component = 'x'
    pressure = pressure
  []
  [u_buoyant]
    type = INSFVMomentumGravity
    variable = vel_x
    rho = 'rho_mixture'
    momentum_component = 'x'
    gravity = '0 ${g} 0'
  []

  [v_time]
    type = INSFVMomentumTimeDerivative
    variable = vel_y
    rho = 'rho_mixture'
    momentum_component = 'y'
  []
  [v_advection]
    type = INSFVMomentumAdvection
    variable = vel_y
    rho = 'rho_mixture'
    momentum_component = 'y'
  []
  [v_viscosity]
    type = INSFVMomentumDiffusion
    variable = vel_y
    mu = 'mu_mixture'
    momentum_component = 'y'
  []
  [v_pressure]
    type = INSFVMomentumPressure
    variable = vel_y
    momentum_component = 'y'
    pressure = pressure
  []
  [v_buoyant]
    type = INSFVMomentumGravity
    variable = vel_y
    rho = 'rho_mixture'
    momentum_component = 'y'
    gravity = '0 ${g} 0'
  []

  [phase_2_time]
    type = FVFunctorTimeKernel
    variable = phase_2
  []
  [phase_2_advection]
    type = INSFVScalarFieldAdvection
    variable = phase_2
    u_slip = 'vel_slip_x'
    v_slip = 'vel_slip_y'
  []
  [phase_2_diffusion]
    type = FVDiffusion
    variable = phase_2
    coeff = 1e-3
  []
[]

[FVBCs]
  [top_x]
    type = INSFVNoSlipWallBC
    variable = vel_x
    boundary = 'top'
    function = ${U_lid}
  []

  [no_slip_x]
    type = INSFVNoSlipWallBC
    variable = vel_x
    boundary = 'left right bottom'
    function = 0
  []

  [no_slip_y]
    type = INSFVNoSlipWallBC
    variable = vel_y
    boundary = 'left right top bottom'
    function = 0
  []

  [bottom_phase_2]
    type = FVDirichletBC
    variable = phase_2
    boundary = 'bottom'
    value = 1.0
  []

  [top_phase_2]
    type = FVDirichletBC
    variable = phase_2
    boundary = 'top'
    value = 0.0
  []
[]

[AuxVariables]
  [U]
    order = CONSTANT
    family = MONOMIAL
    fv = true
  []
  [drag_coefficient]
    type = MooseVariableFVReal
  []
  [rho_mixture_var]
    type = MooseVariableFVReal
  []
  [mu_mixture_var]
    type = MooseVariableFVReal
  []
  [phase_1]
    type = MooseVariableFVReal
  []
[]

[AuxKernels]
  [mag]
    type = VectorMagnitudeAux
    variable = U
    x = vel_x
    y = vel_y
  []
  [populate_cd]
    type = FunctorAux
    variable = drag_coefficient
    functor = 'Darcy_coefficient'
  []
  [populate_rho_mixture_var]
    type = FunctorAux
    variable = rho_mixture_var
    functor = 'rho_mixture'
  []
  [populate_mu_mixture_var]
    type = FunctorAux
    variable = mu_mixture_var
    functor = 'mu_mixture'
  []
  [compute_phase_1]
    type = ParsedAux
    variable = phase_1
    coupled_variables = 'phase_2'
    expression = '1 - phase_2'
  []
[]

[FunctorMaterials]
  [CD]
    type = NSFVDispersePhaseDragFunctorMaterial
    rho = 'rho_mixture'
    mu = mu_mixture
    u = 'vel_x'
    v = 'vel_y'
    particle_diameter = ${dp}
  []
  [mixing_material]
    type = NSFVMixtureFunctorMaterial
    phase_1_names = '${rho_d} ${mu_d}'
    phase_2_names = '${rho} ${mu}'
    prop_names = 'rho_mixture mu_mixture'
    phase_1_fraction = 'phase_2'
  []
  [populate_u_slip]
    type = WCNSFV2PSlipVelocityFunctorMaterial
    slip_velocity_name = 'vel_slip_x'
    momentum_component = 'x'
    u = 'vel_x'
    v = 'vel_y'
    rho = ${rho}
    mu = 'mu_mixture'
    rho_d = ${rho_d}
    particle_diameter = ${dp}
    linear_coef_name = 'Darcy_coefficient'
  []
  [populate_v_slip]
    type = WCNSFV2PSlipVelocityFunctorMaterial
    slip_velocity_name = 'vel_slip_y'
    momentum_component = 'y'
    u = 'vel_x'
    v = 'vel_y'
    rho = ${rho}
    mu = 'mu_mixture'
    rho_d = ${rho_d}
    particle_diameter = ${dp}
    linear_coef_name = 'Darcy_coefficient'
  []
[]

[Postprocessors]
  [average_void]
    type = ElementAverageValue
    variable = 'phase_2'
  []
  [max_y_velocity]
    type = ElementExtremeValue
    variable = 'vel_y'
    value_type = max
  []
  [min_y_velocity]
    type = ElementExtremeValue
    variable = 'vel_y'
    value_type = min
  []
  [max_x_velocity]
    type = ElementExtremeValue
    variable = 'vel_x'
    value_type = max
  []
  [min_x_velocity]
    type = ElementExtremeValue
    variable = 'vel_x'
    value_type = min
  []
  [max_x_slip_velocity]
    type = ElementExtremeFunctorValue
    functor = 'vel_slip_x'
    value_type = max
  []
  [max_y_slip_velocity]
    type = ElementExtremeFunctorValue
    functor = 'vel_slip_y'
    value_type = max
  []
  [max_drag_coefficient]
    type = ElementExtremeFunctorValue
    functor = 'drag_coefficient'
    value_type = max
  []
[]

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

[Executioner]
  type = Transient
  solve_type = 'NEWTON'
  petsc_options_iname = '-pc_type -pc_factor_shift_type'
  petsc_options_value = 'lu       NONZERO'
  [TimeStepper]
    type = IterationAdaptiveDT
    optimal_iterations = 10
    iteration_window = 2
    growth_factor = 2
    cutback_factor = 0.5
    dt = 1e-3
  []
  nl_max_its = 20
  nl_rel_tol = 1e-03
  nl_abs_tol = 1e-9
  l_max_its = 5
  end_time = 1e8
[]

[Outputs]
  exodus = false
  [CSV]
    type = CSV
    execute_on = 'FINAL'
  []
[]

(modules/navier_stokes/test/tests/finite_volume/two_phase/mixture_model/channel-drift-flux.i)

mu = 1.0
rho = 10.0
mu_d = 0.1
rho_d = 1.0
l = 2
U = 1
dp = 0.01
inlet_phase_2 = 0.1
advected_interp_method = 'average'
velocity_interp_method = 'rc'

[GlobalParams]
  rhie_chow_user_object = 'rc'
  density_interp_method = 'average'
  mu_interp_method = 'average'
[]

[UserObjects]
  [rc]
    type = INSFVRhieChowInterpolator
    u = vel_x
    v = vel_y
    pressure = pressure
  []
[]

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 2
    xmin = 0
    xmax = '${fparse l * 5}'
    ymin = '${fparse -l / 2}'
    ymax = '${fparse l / 2}'
    nx = 10
    ny = 4
  []
  uniform_refine = 0
[]

[Variables]
  [vel_x]
    type = INSFVVelocityVariable
    initial_condition = 0
  []
  [vel_y]
    type = INSFVVelocityVariable
    initial_condition = 0
  []
  [pressure]
    type = INSFVPressureVariable
  []
  [phase_2]
    type = INSFVScalarFieldVariable
  []
[]

[FVKernels]

  [mass]
    type = INSFVMassAdvection
    variable = pressure
    advected_interp_method = ${advected_interp_method}
    velocity_interp_method = ${velocity_interp_method}
    rho = 'rho_mixture'
  []

  [u_advection]
    type = INSFVMomentumAdvection
    variable = vel_x
    advected_interp_method = ${advected_interp_method}
    velocity_interp_method = ${velocity_interp_method}
    rho = 'rho_mixture'
    momentum_component = 'x'
  []
  [u_drift]
    type = WCNSFV2PMomentumDriftFlux
    variable = vel_x
    rho_d = ${rho_d}
    fd = 'rho_mixture_var'
    u_slip = 'vel_slip_x'
    v_slip = 'vel_slip_y'
    momentum_component = 'x'
  []
  [u_viscosity]
    type = INSFVMomentumDiffusion
    variable = vel_x
    mu = 'mu_mixture'
    limit_interpolation = true
    momentum_component = 'x'
  []
  [u_pressure]
    type = INSFVMomentumPressure
    variable = vel_x
    momentum_component = 'x'
    pressure = pressure
  []

  [v_advection]
    type = INSFVMomentumAdvection
    variable = vel_y
    advected_interp_method = ${advected_interp_method}
    velocity_interp_method = ${velocity_interp_method}
    rho = 'rho_mixture'
    momentum_component = 'y'
  []
  [v_drift]
    type = WCNSFV2PMomentumDriftFlux
    variable = vel_y
    rho_d = ${rho_d}
    fd = 'rho_mixture_var'
    u_slip = 'vel_slip_x'
    v_slip = 'vel_slip_y'
    momentum_component = 'x'
  []
  [v_viscosity]
    type = INSFVMomentumDiffusion
    variable = vel_y
    mu = 'mu_mixture'
    limit_interpolation = true
    momentum_component = 'y'
  []
  [v_pressure]
    type = INSFVMomentumPressure
    variable = vel_y
    momentum_component = 'y'
    pressure = pressure
  []

  [phase_2_advection]
    type = INSFVScalarFieldAdvection
    variable = phase_2
    u_slip = 'vel_slip_x'
    v_slip = 'vel_slip_y'
    velocity_interp_method = ${velocity_interp_method}
    advected_interp_method = 'upwind'
  []
  [phase_2_src]
    type = NSFVMixturePhaseInterface
    variable = phase_2
    phase_coupled = phase_1
    alpha = 0.1
  []
[]

[FVBCs]
  [inlet-u]
    type = INSFVInletVelocityBC
    boundary = 'left'
    variable = vel_x
    functor = '${U}'
  []
  [inlet-v]
    type = INSFVInletVelocityBC
    boundary = 'left'
    variable = vel_y
    functor = '0'
  []
  [walls-u]
    type = INSFVNoSlipWallBC
    boundary = 'top bottom'
    variable = vel_x
    function = 0
  []
  [walls-v]
    type = INSFVNoSlipWallBC
    boundary = 'top bottom'
    variable = vel_y
    function = 0
  []
  [outlet_p]
    type = INSFVOutletPressureBC
    boundary = 'right'
    variable = pressure
    function = '0'
  []
  [inlet_phase_2]
    type = FVDirichletBC
    boundary = 'left'
    variable = phase_2
    value = ${inlet_phase_2}
  []
[]

[AuxVariables]
  [drag_coefficient]
    type = MooseVariableFVReal
  []
  [rho_mixture_var]
    type = MooseVariableFVReal
  []
  [mu_mixture_var]
    type = MooseVariableFVReal
  []
[]

[AuxKernels]
  [populate_cd]
    type = FunctorAux
    variable = drag_coefficient
    functor = 'Darcy_coefficient'
  []
  [populate_rho_mixture_var]
    type = FunctorAux
    variable = rho_mixture_var
    functor = 'rho_mixture'
  []
  [populate_mu_mixture_var]
    type = FunctorAux
    variable = mu_mixture_var
    functor = 'mu_mixture'
  []
[]

[FunctorMaterials]
  [populate_u_slip]
    type = WCNSFV2PSlipVelocityFunctorMaterial
    slip_velocity_name = 'vel_slip_x'
    momentum_component = 'x'
    u = 'vel_x'
    v = 'vel_y'
    rho = ${rho}
    mu = 'mu_mixture'
    rho_d = ${rho_d}
    particle_diameter = ${dp}
    linear_coef_name = 'Darcy_coefficient'
    outputs = 'out'
    output_properties = 'vel_slip_x'
  []
  [populate_v_slip]
    type = WCNSFV2PSlipVelocityFunctorMaterial
    slip_velocity_name = 'vel_slip_y'
    momentum_component = 'y'
    u = 'vel_x'
    v = 'vel_y'
    rho = ${rho}
    mu = 'mu_mixture'
    rho_d = ${rho_d}
    particle_diameter = ${dp}
    linear_coef_name = 'Darcy_coefficient'
    outputs = 'out'
    output_properties = 'vel_slip_y'
  []
  [compute_phase_1]
    type = ADParsedFunctorMaterial
    property_name = phase_1
    functor_names = 'phase_2'
    expression = '1 - phase_2'
    outputs = 'out'
    output_properties = 'phase_1'
  []
  [CD]
    type = NSFVDispersePhaseDragFunctorMaterial
    rho = 'rho_mixture'
    mu = mu_mixture
    u = 'vel_x'
    v = 'vel_y'
    particle_diameter = ${dp}
  []
  [mixing_material]
    type = NSFVMixtureFunctorMaterial
    phase_2_names = '${rho} ${mu}'
    phase_1_names = '${rho_d} ${mu_d}'
    prop_names = 'rho_mixture mu_mixture'
    phase_1_fraction = 'phase_2'
  []
[]

[Executioner]
  type = Steady
  solve_type = 'NEWTON'
  nl_rel_tol = 1e-10
[]

[Preconditioning]
  [SMP]
    type = SMP
    full = true
    petsc_options_iname = '-pc_type -pc_factor_shift_type'
    petsc_options_value = 'lu       NONZERO'
  []
[]

[Outputs]
  print_linear_residuals = true
  print_nonlinear_residuals = true
  [out]
    type = Exodus
    hide = 'Re lin cum_lin'
  []
  [perf]
    type = PerfGraphOutput
  []
[]

[Postprocessors]
  [Re]
    type = ParsedPostprocessor
    function = '${rho} * ${l} * ${U}'
    pp_names = ''
  []
  [lin]
    type = NumLinearIterations
  []
  [cum_lin]
    type = CumulativeValuePostprocessor
    postprocessor = lin
  []
[]

(modules/navier_stokes/test/tests/finite_volume/two_phase/mixture_model/channel-advection-slip.i)

mu = 1.0
rho = 10.0
mu_d = 0.1
rho_d = 1.0
l = 2
U = 1
dp = 0.01
inlet_phase_2 = 0.1
advected_interp_method = 'average'
velocity_interp_method = 'rc'

[GlobalParams]
  rhie_chow_user_object = 'rc'
  mu_interp_method = 'average'
[]

[UserObjects]
  [rc]
    type = INSFVRhieChowInterpolator
    u = vel_x
    v = vel_y
    pressure = pressure
  []
[]

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 2
    xmin = 0
    xmax = '${fparse l * 5}'
    ymin = '${fparse -l / 2}'
    ymax = '${fparse l / 2}'
    nx = 10
    ny = 6
  []
  uniform_refine = 0
[]

[Variables]
  [vel_x]
    type = INSFVVelocityVariable
    initial_condition = 0
  []
  [vel_y]
    type = INSFVVelocityVariable
    initial_condition = 0
  []
  [pressure]
    type = INSFVPressureVariable
  []
  [phase_2]
    type = INSFVScalarFieldVariable
  []
[]

[FVKernels]

  [mass]
    type = INSFVMassAdvection
    variable = pressure
    advected_interp_method = ${advected_interp_method}
    velocity_interp_method = ${velocity_interp_method}
    rho = 'rho_mixture'
  []

  [u_advection]
    type = INSFVMomentumAdvection
    variable = vel_x
    advected_interp_method = ${advected_interp_method}
    velocity_interp_method = ${velocity_interp_method}
    rho = 'rho_mixture'
    momentum_component = 'x'
  []
  [u_advection_slip]
    type = WCNSFV2PMomentumAdvectionSlip
    variable = vel_x
    advected_interp_method = ${advected_interp_method}
    velocity_interp_method = ${velocity_interp_method}
    rho = 'rho_mixture'
    rho_d = ${rho_d}
    fd = 0.5
    u_slip = 'vel_slip_x'
    v_slip = 'vel_slip_y'
    momentum_component = 'x'
  []
  [u_viscosity]
    type = INSFVMomentumDiffusion
    variable = vel_x
    mu = 'mu_mixture'
    limit_interpolation = true
    momentum_component = 'x'
  []
  [u_pressure]
    type = INSFVMomentumPressure
    variable = vel_x
    momentum_component = 'x'
    pressure = pressure
  []

  [v_advection]
    type = INSFVMomentumAdvection
    variable = vel_y
    advected_interp_method = ${advected_interp_method}
    velocity_interp_method = ${velocity_interp_method}
    rho = 'rho_mixture'
    momentum_component = 'y'
  []
  [v_advection_slip]
    type = WCNSFV2PMomentumAdvectionSlip
    variable = vel_y
    advected_interp_method = ${advected_interp_method}
    velocity_interp_method = ${velocity_interp_method}
    rho = ${rho}
    rho_d = ${rho_d}
    fd = 0.5
    u_slip = 'vel_slip_x'
    v_slip = 'vel_slip_y'
    momentum_component = 'y'
  []
  [v_viscosity]
    type = INSFVMomentumDiffusion
    variable = vel_y
    mu = 'mu_mixture'
    limit_interpolation = true
    momentum_component = 'y'
  []
  [v_pressure]
    type = INSFVMomentumPressure
    variable = vel_y
    momentum_component = 'y'
    pressure = pressure
  []

  [phase_2_advection]
    type = INSFVScalarFieldAdvection
    variable = phase_2
    u_slip = 'vel_slip_x'
    v_slip = 'vel_slip_y'
    velocity_interp_method = ${velocity_interp_method}
    advected_interp_method = 'upwind'
  []
  [phase_2_src]
    type = NSFVMixturePhaseInterface
    variable = phase_2
    phase_coupled = phase_1
    alpha = 0.1
  []
[]

[FVBCs]
  [inlet-u]
    type = INSFVInletVelocityBC
    boundary = 'left'
    variable = vel_x
    functor = '${U}'
  []
  [inlet-v]
    type = INSFVInletVelocityBC
    boundary = 'left'
    variable = vel_y
    functor = '0'
  []
  [walls-u]
    type = INSFVNoSlipWallBC
    boundary = 'top bottom'
    variable = vel_x
    function = 0
  []
  [walls-v]
    type = INSFVNoSlipWallBC
    boundary = 'top bottom'
    variable = vel_y
    function = 0
  []
  [outlet_p]
    type = INSFVOutletPressureBC
    boundary = 'right'
    variable = pressure
    function = '0'
  []
  [inlet_phase_2]
    type = FVDirichletBC
    boundary = 'left'
    variable = phase_2
    value = ${inlet_phase_2}
  []
[]

[AuxVariables]
  [drag_coefficient]
    type = MooseVariableFVReal
  []
  [rho_mixture_var]
    type = MooseVariableFVReal
  []
  [mu_mixture_var]
    type = MooseVariableFVReal
  []
[]

[AuxKernels]
  [populate_cd]
    type = FunctorAux
    variable = drag_coefficient
    functor = 'Darcy_coefficient'
  []
  [populate_rho_mixture_var]
    type = FunctorAux
    variable = rho_mixture_var
    functor = 'rho_mixture'
  []
  [populate_mu_mixture_var]
    type = FunctorAux
    variable = mu_mixture_var
    functor = 'mu_mixture'
  []
[]

[FunctorMaterials]
  [phase_1]
    property_name = 'phase_1'
    type = ADParsedFunctorMaterial
    functor_names = 'phase_2'
    expression = '1 - phase_2'
    outputs = 'out'
    output_properties = 'phase_1'
  []
  [populate_u_slip]
    type = WCNSFV2PSlipVelocityFunctorMaterial
    slip_velocity_name = 'vel_slip_x'
    momentum_component = 'x'
    u = 'vel_x'
    v = 'vel_y'
    rho = ${rho}
    mu = 'mu_mixture'
    rho_d = ${rho_d}
    particle_diameter = ${dp}
    linear_coef_name = 'Darcy_coefficient'
    outputs = 'out'
    output_properties = 'vel_slip_x'
  []
  [populate_v_slip]
    type = WCNSFV2PSlipVelocityFunctorMaterial
    slip_velocity_name = 'vel_slip_y'
    momentum_component = 'y'
    u = 'vel_x'
    v = 'vel_y'
    rho = ${rho}
    mu = 'mu_mixture'
    rho_d = ${rho_d}
    particle_diameter = ${dp}
    linear_coef_name = 'Darcy_coefficient'
    outputs = 'out'
    output_properties = 'vel_slip_y'
  []
  [CD]
    type = NSFVDispersePhaseDragFunctorMaterial
    rho = 'rho_mixture'
    mu = mu_mixture
    u = 'vel_x'
    v = 'vel_y'
    particle_diameter = ${dp}
  []
  [mixing_material]
    type = NSFVMixtureFunctorMaterial
    phase_2_names = '${rho} ${mu}'
    phase_1_names = '${rho_d} ${mu_d}'
    prop_names = 'rho_mixture mu_mixture'
    phase_1_fraction = 'phase_2'
  []
[]

[Executioner]
  type = Steady
  solve_type = 'NEWTON'
  nl_rel_tol = 1e-10
[]

[Preconditioning]
  [SMP]
    type = SMP
    full = true
    petsc_options_iname = '-pc_type -pc_factor_shift_type'
    petsc_options_value = 'lu       NONZERO'
  []
[]

[Outputs]
  [out]
    type = Exodus
    hide = 'Re lin cum_lin'
  []
[]

[Postprocessors]
  [Re]
    type = ParsedPostprocessor
    function = '${rho} * ${l} * ${U}'
    pp_names = ''
  []
  [lin]
    type = NumLinearIterations
  []
  [cum_lin]
    type = CumulativeValuePostprocessor
    postprocessor = lin
  []
[]

(modules/navier_stokes/test/tests/finite_volume/two_phase/mixture_model/channel-drift-flux-transient.i)

mu = 1.0
rho = 10.0
mu_d = 0.1
rho_d = 1.0
l = 2
U = 1
dp = 0.01
inlet_phase_2 = 0.1
advected_interp_method = 'average'
velocity_interp_method = 'rc'

[GlobalParams]
  rhie_chow_user_object = 'rc'
  density_interp_method = 'average'
  mu_interp_method = 'average'
[]

[UserObjects]
  [rc]
    type = INSFVRhieChowInterpolator
    u = vel_x
    v = vel_y
    pressure = pressure
  []
[]

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 2
    xmin = 0
    xmax = '${fparse l * 5}'
    ymin = '${fparse -l / 2}'
    ymax = '${fparse l / 2}'
    nx = 10
    ny = 4
  []
  uniform_refine = 0
[]

[Variables]
  [vel_x]
    type = INSFVVelocityVariable
    initial_condition = 0
  []
  [vel_y]
    type = INSFVVelocityVariable
    initial_condition = 0
  []
  [pressure]
    type = INSFVPressureVariable
  []
  [phase_2]
    type = INSFVScalarFieldVariable
  []
[]

[FVKernels]

  [mass]
    type = INSFVMassAdvection
    variable = pressure
    advected_interp_method = ${advected_interp_method}
    velocity_interp_method = ${velocity_interp_method}
    rho = 'rho_mixture'
  []

  [u_time]
    type = INSFVMomentumTimeDerivative
    variable = vel_x
    rho = 'rho_mixture'
    momentum_component = 'x'
  []
  [u_advection]
    type = INSFVMomentumAdvection
    variable = vel_x
    advected_interp_method = ${advected_interp_method}
    velocity_interp_method = ${velocity_interp_method}
    rho = 'rho_mixture'
    momentum_component = 'x'
  []
  [u_drift]
    type = WCNSFV2PMomentumDriftFlux
    variable = vel_x
    rho_d = ${rho_d}
    fd = 'rho_mixture_var'
    u_slip = 'vel_slip_x'
    v_slip = 'vel_slip_y'
    momentum_component = 'x'
  []
  [u_viscosity]
    type = INSFVMomentumDiffusion
    variable = vel_x
    mu = 'mu_mixture'
    limit_interpolation = true
    momentum_component = 'x'
  []
  [u_pressure]
    type = INSFVMomentumPressure
    variable = vel_x
    momentum_component = 'x'
    pressure = pressure
  []

  [v_time]
    type = INSFVMomentumTimeDerivative
    variable = vel_y
    rho = 'rho_mixture'
    momentum_component = 'y'
  []
  [v_advection]
    type = INSFVMomentumAdvection
    variable = vel_y
    advected_interp_method = ${advected_interp_method}
    velocity_interp_method = ${velocity_interp_method}
    rho = 'rho_mixture'
    momentum_component = 'y'
  []
  [v_drift]
    type = WCNSFV2PMomentumDriftFlux
    variable = vel_y
    rho_d = ${rho_d}
    fd = 'rho_mixture_var'
    u_slip = 'vel_slip_x'
    v_slip = 'vel_slip_y'
    momentum_component = 'y'
  []
  [v_viscosity]
    type = INSFVMomentumDiffusion
    variable = vel_y
    mu = 'mu_mixture'
    limit_interpolation = true
    momentum_component = 'y'
  []
  [v_pressure]
    type = INSFVMomentumPressure
    variable = vel_y
    momentum_component = 'y'
    pressure = pressure
  []

  [phase_2_time]
    type = FVFunctorTimeKernel
    variable = phase_2
    functor = phase_2
  []
  [phase_2_advection]
    type = INSFVScalarFieldAdvection
    variable = phase_2
    u_slip = 'vel_x'
    v_slip = 'vel_y'
    velocity_interp_method = ${velocity_interp_method}
    advected_interp_method = 'upwind'
  []
  [phase_2_src]
    type = NSFVMixturePhaseInterface
    variable = phase_2
    phase_coupled = phase_1
    alpha = 0.1
  []
[]

[FVBCs]
  [inlet-u]
    type = INSFVInletVelocityBC
    boundary = 'left'
    variable = vel_x
    functor = '${U}'
  []
  [inlet-v]
    type = INSFVInletVelocityBC
    boundary = 'left'
    variable = vel_y
    functor = '0'
  []
  [walls-u]
    type = INSFVNoSlipWallBC
    boundary = 'top bottom'
    variable = vel_x
    function = 0
  []
  [walls-v]
    type = INSFVNoSlipWallBC
    boundary = 'top bottom'
    variable = vel_y
    function = 0
  []
  [outlet_p]
    type = INSFVOutletPressureBC
    boundary = 'right'
    variable = pressure
    function = '0'
  []
  [inlet_phase_2]
    type = FVDirichletBC
    boundary = 'left'
    variable = phase_2
    value = ${inlet_phase_2}
  []
[]

[AuxVariables]
  [drag_coefficient]
    type = MooseVariableFVReal
  []
  [rho_mixture_var]
    type = MooseVariableFVReal
  []
  [mu_mixture_var]
    type = MooseVariableFVReal
  []
[]

[AuxKernels]
  [populate_cd]
    type = FunctorAux
    variable = drag_coefficient
    functor = 'Darcy_coefficient'
  []
  [populate_rho_mixture_var]
    type = FunctorAux
    variable = rho_mixture_var
    functor = 'rho_mixture'
  []
  [populate_mu_mixture_var]
    type = FunctorAux
    variable = mu_mixture_var
    functor = 'mu_mixture'
  []
[]

[FunctorMaterials]
  [populate_u_slip]
    type = WCNSFV2PSlipVelocityFunctorMaterial
    slip_velocity_name = 'vel_slip_x'
    momentum_component = 'x'
    u = 'vel_x'
    v = 'vel_y'
    rho = ${rho}
    mu = 'mu_mixture'
    rho_d = ${rho_d}
    particle_diameter = ${dp}
    linear_coef_name = 'Darcy_coefficient'
  []
  [populate_v_slip]
    type = WCNSFV2PSlipVelocityFunctorMaterial
    slip_velocity_name = 'vel_slip_y'
    momentum_component = 'y'
    u = 'vel_x'
    v = 'vel_y'
    rho = ${rho}
    mu = 'mu_mixture'
    rho_d = ${rho_d}
    particle_diameter = ${dp}
    linear_coef_name = 'Darcy_coefficient'
  []
  [compute_phase_1]
    type = ADParsedFunctorMaterial
    property_name = phase_1
    functor_names = 'phase_2'
    expression = '1 - phase_2'
  []
  [CD]
    type = NSFVDispersePhaseDragFunctorMaterial
    rho = 'rho_mixture'
    mu = mu_mixture
    u = 'vel_x'
    v = 'vel_y'
    particle_diameter = ${dp}
  []
  [mixing_material]
    type = NSFVMixtureFunctorMaterial
    phase_2_names = '${rho} ${mu}'
    phase_1_names = '${rho_d} ${mu_d}'
    prop_names = 'rho_mixture mu_mixture'
    phase_1_fraction = 'phase_2'
  []
[]

[Executioner]
  type = Transient
  solve_type = 'NEWTON'
  nl_rel_tol = 1e-10
  dt = 0.1
  end_time = 1.0
[]

[Preconditioning]
  [SMP]
    type = SMP
    full = true
    petsc_options_iname = '-pc_type -pc_factor_shift_type'
    petsc_options_value = 'lu       NONZERO'
  []
[]

[Outputs]
  exodus = false
  [CSV]
    type = CSV
    execute_on = 'TIMESTEP_END'
  []
[]

[Postprocessors]
  [Re]
    type = ParsedPostprocessor
    function = '${rho} * ${l} * ${U}'
    pp_names = ''
  []
  [rho_outlet]
    type = SideAverageValue
    boundary = 'right'
    variable = 'rho_mixture_var'
  []
[]

(modules/navier_stokes/test/tests/finite_volume/two_phase/mixture_model/lid-driven-two-phase.i)

mu = 1.0
rho = 1.0e3
mu_d = 0.3
rho_d = 1.0
dp = 0.01
U_lid = 0.1
g = -9.81

[GlobalParams]
  velocity_interp_method = 'rc'
  advected_interp_method = 'upwind'
  rhie_chow_user_object = 'rc'
[]

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 2
    xmin = 0
    xmax = .1
    ymin = 0
    ymax = .1
    nx = 10
    ny = 10
  []
[]

[Variables]
  [vel_x]
    type = INSFVVelocityVariable
  []
  [vel_y]
    type = INSFVVelocityVariable
  []
  [pressure]
    type = INSFVPressureVariable
  []
  [phase_2]
    type = INSFVScalarFieldVariable
  []
[]

[UserObjects]
  [rc]
    type = INSFVRhieChowInterpolator
    u = vel_x
    v = vel_y
    pressure = pressure
  []
  [pin_pressure]
    type = NSPressurePin
    variable = pressure
    pin_type = point-value
    point = '0 0 0'
  []
[]

[FVKernels]
  [mass]
    type = INSFVMassAdvection
    variable = pressure
    rho = 'rho_mixture'
  []

  [u_time]
    type = INSFVMomentumTimeDerivative
    variable = vel_x
    rho = 'rho_mixture'
    momentum_component = 'x'
  []
  [u_advection]
    type = INSFVMomentumAdvection
    variable = vel_x
    rho = 'rho_mixture'
    momentum_component = 'x'
  []
  [u_viscosity]
    type = INSFVMomentumDiffusion
    variable = vel_x
    mu = 'mu_mixture'
    momentum_component = 'x'
  []
  [u_pressure]
    type = INSFVMomentumPressure
    variable = vel_x
    momentum_component = 'x'
    pressure = pressure
  []
  [u_buoyant]
    type = INSFVMomentumGravity
    variable = vel_x
    rho = 'rho_mixture'
    momentum_component = 'x'
    gravity = '0 ${g} 0'
  []

  [v_time]
    type = INSFVMomentumTimeDerivative
    variable = vel_y
    rho = 'rho_mixture'
    momentum_component = 'y'
  []
  [v_advection]
    type = INSFVMomentumAdvection
    variable = vel_y
    rho = 'rho_mixture'
    momentum_component = 'y'
  []
  [v_viscosity]
    type = INSFVMomentumDiffusion
    variable = vel_y
    mu = 'mu_mixture'
    momentum_component = 'y'
  []
  [v_pressure]
    type = INSFVMomentumPressure
    variable = vel_y
    momentum_component = 'y'
    pressure = pressure
  []
  [v_buoyant]
    type = INSFVMomentumGravity
    variable = vel_y
    rho = 'rho_mixture'
    momentum_component = 'y'
    gravity = '0 ${g} 0'
  []

  [phase_2_time]
    type = FVFunctorTimeKernel
    variable = phase_2
  []
  [phase_2_advection]
    type = INSFVScalarFieldAdvection
    variable = phase_2
    u_slip = 'vel_slip_x'
    v_slip = 'vel_slip_y'
  []
  [phase_2_diffusion]
    type = FVDiffusion
    variable = phase_2
    coeff = 1e-3
  []
[]

[FVBCs]
  [top_x]
    type = INSFVNoSlipWallBC
    variable = vel_x
    boundary = 'top'
    function = ${U_lid}
  []

  [no_slip_x]
    type = INSFVNoSlipWallBC
    variable = vel_x
    boundary = 'left right bottom'
    function = 0
  []

  [no_slip_y]
    type = INSFVNoSlipWallBC
    variable = vel_y
    boundary = 'left right top bottom'
    function = 0
  []

  [bottom_phase_2]
    type = FVDirichletBC
    variable = phase_2
    boundary = 'bottom'
    value = 1.0
  []

  [top_phase_2]
    type = FVDirichletBC
    variable = phase_2
    boundary = 'top'
    value = 0.0
  []
[]

[AuxVariables]
  [U]
    order = CONSTANT
    family = MONOMIAL
    fv = true
  []
  [drag_coefficient]
    type = MooseVariableFVReal
  []
  [rho_mixture_var]
    type = MooseVariableFVReal
  []
  [mu_mixture_var]
    type = MooseVariableFVReal
  []
[]

[AuxKernels]
  [mag]
    type = VectorMagnitudeAux
    variable = U
    x = vel_x
    y = vel_y
  []
  [populate_cd]
    type = FunctorAux
    variable = drag_coefficient
    functor = 'Darcy_coefficient'
  []
  [populate_rho_mixture_var]
    type = FunctorAux
    variable = rho_mixture_var
    functor = 'rho_mixture'
  []
  [populate_mu_mixture_var]
    type = FunctorAux
    variable = mu_mixture_var
    functor = 'mu_mixture'
  []
[]

[FunctorMaterials]
  [populate_u_slip]
    type = WCNSFV2PSlipVelocityFunctorMaterial
    slip_velocity_name = 'vel_slip_x'
    momentum_component = 'x'
    u = 'vel_x'
    v = 'vel_y'
    rho = ${rho}
    mu = 'mu_mixture'
    rho_d = ${rho_d}
    particle_diameter = ${dp}
    linear_coef_name = 'Darcy_coefficient'
  []
  [populate_v_slip]
    type = WCNSFV2PSlipVelocityFunctorMaterial
    slip_velocity_name = 'vel_slip_y'
    momentum_component = 'y'
    u = 'vel_x'
    v = 'vel_y'
    rho = ${rho}
    mu = 'mu_mixture'
    rho_d = ${rho_d}
    particle_diameter = ${dp}
    linear_coef_name = 'Darcy_coefficient'
  []
  [compute_phase_1]
    type = ADParsedFunctorMaterial
    property_name = phase_1
    functor_names = 'phase_2'
    expression = '1 - phase_2'
  []
  [CD]
    type = NSFVDispersePhaseDragFunctorMaterial
    rho = 'rho_mixture'
    mu = mu_mixture
    u = 'vel_x'
    v = 'vel_y'
    particle_diameter = ${dp}
  []
  [mixing_material]
    type = NSFVMixtureFunctorMaterial
    phase_1_names = '${rho_d} ${mu_d}'
    phase_2_names = '${rho} ${mu}'
    prop_names = 'rho_mixture mu_mixture'
    phase_1_fraction = 'phase_2'
  []
[]

[Postprocessors]
  [average_void]
    type = ElementAverageValue
    variable = 'phase_2'
  []
  [max_y_velocity]
    type = ElementExtremeValue
    variable = 'vel_y'
    value_type = max
  []
  [min_y_velocity]
    type = ElementExtremeValue
    variable = 'vel_y'
    value_type = min
  []
  [max_x_velocity]
    type = ElementExtremeValue
    variable = 'vel_x'
    value_type = max
  []
  [min_x_velocity]
    type = ElementExtremeValue
    variable = 'vel_x'
    value_type = min
  []
  [max_x_slip_velocity]
    type = ElementExtremeFunctorValue
    functor = 'vel_slip_x'
    value_type = max
  []
  [max_y_slip_velocity]
    type = ElementExtremeFunctorValue
    functor = 'vel_slip_y'
    value_type = max
  []
  [max_drag_coefficient]
    type = ElementExtremeFunctorValue
    functor = 'drag_coefficient'
    value_type = max
  []
[]

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

[Executioner]
  type = Transient
  solve_type = 'NEWTON'
  petsc_options_iname = '-pc_type -pc_factor_shift_type'
  petsc_options_value = 'lu NONZERO'
  [TimeStepper]
    type = IterationAdaptiveDT
    optimal_iterations = 7
    iteration_window = 2
    growth_factor = 2.0
    cutback_factor = 0.5
    dt = 1e-3
  []
  nl_max_its = 10
  nl_rel_tol = 1e-03
  nl_abs_tol = 1e-9
  l_max_its = 5
  end_time = 1e8
[]

[Outputs]
  exodus = false
  [CSV]
    type = CSV
    execute_on = 'FINAL'
  []
[]

Input Parameters
Input Files
References