LinearFVScalarAdvection

This kernel adds the contributions of the scalar advection term to the matrix and right hand side of the scalar equation system for the finite volume SIMPLE segregated solver SIMPLE.

This term is described by $var element = document.getElementById("moose-equation-83f934f1-86f1-4931-81b0-90149106bb84");katex.render("\\nabla \\cdot \\left(\\vec{u} C_i \\right)", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ present in the scalar equation conservation for an incompressible/weakly-compressible formulation.

For FV, the integral of the advection term of scalar $var element = document.getElementById("moose-equation-486dcb70-cc81-44d5-86f8-4ce0b9d2da72");katex.render("C_i", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ over a cell can be expressed as:

$var element = document.getElementById("moose-equation-623278b2-f3f0-4a3a-918b-08e1ab63fc93");katex.render("\\int\\limits_{V_C} \\nabla \\cdot \\left(\\vec{u} C_i \\right) dV \\approx \\sum\\limits_f ( \\vec{u}\\cdot \\vec{n})_{RC} C_if |S_f| \\,", element, {displayMode:true,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$

where $var element = document.getElementById("moose-equation-d49f698b-49a7-468b-b9dc-ffbedd34973b");katex.render("C_{if}", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ is the face value of the scalar concentration. An interpolation scheme (e.g. upwind) can be used to compute the face value. This kernel adds the face contribution for each face $var element = document.getElementById("moose-equation-56221589-92e1-485c-b3dd-6bb56c4fdb47");katex.render("f", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ to the right hand side and matrix.

The volumetric face flux $var element = document.getElementById("moose-equation-3dd80ede-2f5a-4d59-a676-aaee0c8ff2a9");katex.render("(\\vec{u}\\cdot \\vec{n})_{RC}", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ is provided by the RhieChowMassFlux object which uses pressure gradients and the discrete momentum equation to compute face velocities and mass fluxes. For more information on the expression that is used, see SIMPLE.

Input Parameters

rhie_chow_user_objectThe rhie-chow user-object which is used to determine the face velocity.
C++ Type:UserObjectName
Controllable:No
Description:The rhie-chow user-object which is used to determine the face velocity.
variableThe name of the variable whose linear system this object contributes to
C++ Type:LinearVariableName
Unit:(no unit assumed)
Controllable:No
Description:The name of the variable whose linear system this object contributes to

Required Parameters

advected_interp_methodupwindThe interpolation to use for the advected quantity. Options are 'upwind', 'average', 'sou' (for second-order upwind), 'min_mod', 'vanLeer', 'quick', 'venkatakrishnan', and 'skewness-corrected' with the default being 'upwind'.
Default:upwind
C++ Type:MooseEnum
Options:average, upwind, sou, min_mod, vanLeer, quick, venkatakrishnan, skewness-corrected
Controllable:No
Description:The interpolation to use for the advected quantity. Options are 'upwind', 'average', 'sou' (for second-order upwind), 'min_mod', 'vanLeer', 'quick', 'venkatakrishnan', and 'skewness-corrected' with the default being 'upwind'.
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
force_boundary_executionFalseWhether to force execution of this object on all external boundaries.
Default:False
C++ Type:bool
Controllable:No
Description:Whether to force execution of this object on all external boundaries.
matrix_onlyFalseWhether this object is only doing assembly to matrices (no vectors)
Default:False
C++ Type:bool
Controllable:No
Description:Whether this object is only doing assembly to matrices (no vectors)
u_slipThe slip-velocity in the x direction. A functor is any of the following: a variable, a functor material property, a function, a postprocessor or a number.
C++ Type:MooseFunctorName
Unit:(no unit assumed)
Controllable:No
Description:The slip-velocity in the x direction. A functor is any of the following: a variable, a functor material property, a function, a postprocessor or a number.
v_slipThe slip-velocity in the y direction. A functor is any of the following: a variable, a functor material property, a function, a postprocessor or a number.
C++ Type:MooseFunctorName
Unit:(no unit assumed)
Controllable:No
Description:The slip-velocity in the y direction. A functor is any of the following: a variable, a functor material property, a function, a postprocessor or a number.
w_slipThe slip-velocity in the z direction. A functor is any of the following: a variable, a functor material property, a function, a postprocessor or a number.
C++ Type:MooseFunctorName
Unit:(no unit assumed)
Controllable:No
Description:The slip-velocity in the z direction. A functor is any of the following: a variable, a functor material property, a function, a postprocessor or a number.

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>
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>
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>
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
Options:nontime, system
Controllable:No
Description:The tag for the matrices this Kernel should fill
vector_tagsrhsThe tag for the vectors this Kernel should fill
Default:rhs
C++ Type:MultiMooseEnum
Options:rhs, time
Controllable:No
Description:The tag for the vectors this Kernel should fill

Contribution To Tagged Field Data 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
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

ghost_layers1The number of layers of elements to ghost.
Default:1
C++ Type:unsigned short
Controllable:No
Description:The number of layers of elements to ghost.
use_point_neighborsFalseWhether to use point neighbors, which introduces additional ghosting to that used for simple face neighbors.
Default:False
C++ Type:bool
Controllable:No
Description:Whether to use point neighbors, which introduces additional ghosting to that used for simple face neighbors.

Parallel Ghosting Parameters

Input Files

(modules/navier_stokes/test/tests/finite_volume/two_phase/mixture_model/segregated/channel-drift-flux.i)
(modules/navier_stokes/test/tests/finite_volume/ins/channel-flow/linear-segregated/2d-scalar/channel.i)

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

mu = 1.0
rho = 10.0
mu_d = 0.1
rho_d = 1.0
l = 2
# 'average' leads to slight oscillations, upwind may be preferred
# This method is selected for consistency with the original nonlinear input
advected_interp_method = 'average'

# TODO remove need for those
cp = 1
k = 1
cp_d = 1
k_d = 1

[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
[]

[Problem]
  linear_sys_names = 'u_system v_system pressure_system phi_system'
  previous_nl_solution_required = true
[]

[Variables]
  [vel_x]
    type = MooseLinearVariableFVReal
    solver_sys = u_system
    initial_condition = 1
  []
  [vel_y]
    type = MooseLinearVariableFVReal
    solver_sys = v_system
  []
  [pressure]
    type = MooseLinearVariableFVReal
    solver_sys = pressure_system
  []
  [phase_2]
    type = MooseLinearVariableFVReal
    solver_sys = phi_system
  []
[]

[LinearFVKernels]
  [flow_p_diffusion]
    type = LinearFVAnisotropicDiffusion
    diffusion_tensor = Ainv
    use_nonorthogonal_correction = false
    variable = pressure
  []
  [flow_HbyA_divergence]
    type = LinearFVDivergence
    face_flux = HbyA
    force_boundary_execution = true
    variable = pressure
  []
  [flow_ins_momentum_flux_x]
    type = LinearWCNSFVMomentumFlux
    advected_interp_method = ${advected_interp_method}
    momentum_component = x
    mu = mu_mixture
    rhie_chow_user_object = ins_rhie_chow_interpolator
    u = vel_x
    use_deviatoric_terms = false
    use_nonorthogonal_correction = false
    v = vel_y
    variable = vel_x
  []
  [flow_ins_momentum_flux_y]
    type = LinearWCNSFVMomentumFlux
    advected_interp_method = ${advected_interp_method}
    momentum_component = y
    mu = mu_mixture
    rhie_chow_user_object = ins_rhie_chow_interpolator
    u = vel_x
    use_deviatoric_terms = false
    use_nonorthogonal_correction = false
    v = vel_y
    variable = vel_y
  []
  [mixture_drift_flux_x]
    type = LinearWCNSFV2PMomentumDriftFlux
    density_interp_method = average
    fraction_dispersed = phase_2
    momentum_component = x
    rhie_chow_user_object = ins_rhie_chow_interpolator
    rho_d = ${rho_d}
    u_slip = vel_slip_x
    v_slip = vel_slip_y
    variable = vel_x
  []
  [mixture_drift_flux_y]
    type = LinearWCNSFV2PMomentumDriftFlux
    density_interp_method = average
    fraction_dispersed = phase_2
    momentum_component = y
    rhie_chow_user_object = ins_rhie_chow_interpolator
    rho_d = ${rho_d}
    u_slip = vel_slip_x
    v_slip = vel_slip_y
    variable = vel_y
  []
  [flow_ins_momentum_pressure_x]
    type = LinearFVMomentumPressure
    momentum_component = x
    pressure = pressure
    variable = vel_x
  []
  [flow_ins_momentum_pressure_y]
    type = LinearFVMomentumPressure
    momentum_component = y
    pressure = pressure
    variable = vel_y
  []
  [flow_momentum_friction_0_x]
    type = LinearFVMomentumFriction
    Darcy_name = Darcy_coefficient_vec
    momentum_component = x
    mu = mu_mixture
    variable = vel_x
  []
  [flow_momentum_friction_0_y]
    type = LinearFVMomentumFriction
    Darcy_name = Darcy_coefficient_vec
    momentum_component = y
    mu = mu_mixture
    variable = vel_y
  []

  # Mixture phase equation
  [mixture_ins_phase_2_advection]
    type = LinearFVScalarAdvection
    advected_interp_method = upwind
    rhie_chow_user_object = ins_rhie_chow_interpolator
    u_slip = vel_slip_x
    v_slip = vel_slip_y
    variable = phase_2
  []
  [mixture_phase_interface_reaction]
    type = LinearFVReaction
    coeff = 0.1
    variable = phase_2
  []
  [mixture_phase_interface_source]
    type = LinearFVSource
    scaling_factor = 0.1
    source_density = phase_1
    variable = phase_2
  []
[]

[LinearFVBCs]
  [vel_x_left]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = left
    functor = 1
    variable = vel_x
  []
  [vel_y_left]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = left
    functor = 0
    variable = vel_y
  []
  [pressure_extrapolation_inlet_left]
    type = LinearFVExtrapolatedPressureBC
    boundary = left
    use_two_term_expansion = true
    variable = pressure
  []
  [vel_x_right]
    type = LinearFVAdvectionDiffusionOutflowBC
    boundary = right
    use_two_term_expansion = true
    variable = vel_x
  []
  [vel_y_right]
    type = LinearFVAdvectionDiffusionOutflowBC
    boundary = right
    use_two_term_expansion = true
    variable = vel_y
  []
  [pressure_right]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = right
    functor = 0
    variable = pressure
  []
  [vel_x_bottom]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = bottom
    functor = 0
    variable = vel_x
  []
  [vel_y_bottom]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = bottom
    functor = 0
    variable = vel_y
  []
  [vel_x_top]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = top
    functor = 0
    variable = vel_x
  []
  [vel_y_top]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = top
    functor = 0
    variable = vel_y
  []
  [pressure_extrapolation_top_bottom]
    type = LinearFVExtrapolatedPressureBC
    boundary = 'top bottom'
    use_two_term_expansion = true
    variable = pressure
  []

  [phase_2_left]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = left
    functor = 0.1
    variable = phase_2
  []
  [phase_2_right]
    type = LinearFVAdvectionDiffusionOutflowBC
    boundary = right
    use_two_term_expansion = true
    variable = phase_2
  []
[]

[FunctorMaterials]
  [flow_ins_speed_material]
    type = ADVectorMagnitudeFunctorMaterial
    execute_on = ALWAYS
    outputs = none
    vector_magnitude_name = speed
    x_functor = vel_x
    y_functor = vel_y
  []

  [mixture_phase_1_fraction]
    type = ParsedFunctorMaterial
    execute_on = ALWAYS
    expression = '1 - phase_2'
    functor_names = phase_2
    output_properties = phase_1
    outputs = all
    property_name = phase_1
  []
  [mixture_mixture_material]
    type = WCNSLinearFVMixtureFunctorMaterial
    execute_on = ALWAYS
    limit_phase_fraction = true
    outputs = all
    phase_1_fraction = phase_2
    phase_1_names = '${rho_d} ${mu_d} ${cp_d} ${k_d}'
    phase_2_names = '${rho}   ${mu}   ${cp}   ${k}'
    prop_names = 'rho_mixture mu_mixture cp_mixture k_mixture'
  []
  [mixture_slip_x]
    type = WCNSFV2PSlipVelocityFunctorMaterial
    execute_on = ALWAYS
    gravity = '0 0 0'
    linear_coef_name = Darcy_coefficient
    momentum_component = x
    mu = mu_mixture
    outputs = all
    particle_diameter = 0.01
    rho = ${rho}
    rho_d = ${rho_d}
    slip_velocity_name = vel_slip_x
    u = vel_x
    v = vel_y
  []
  [mixture_slip_y]
    type = WCNSFV2PSlipVelocityFunctorMaterial
    execute_on = ALWAYS
    gravity = '0 0 0'
    linear_coef_name = Darcy_coefficient
    momentum_component = y
    mu = mu_mixture
    outputs = all
    particle_diameter = 0.01
    rho = ${rho}
    rho_d = ${rho_d}
    slip_velocity_name = vel_slip_y
    u = vel_x
    v = vel_y
  []
  [mixture_dispersed_drag]
    type = NSFVDispersePhaseDragFunctorMaterial
    drag_coef_name = Darcy_coefficient
    execute_on = ALWAYS
    mu = mu_mixture
    outputs = all
    particle_diameter = 0.01
    rho = rho_mixture
    u = vel_x
    v = vel_y
  []
[]

[UserObjects]
  [ins_rhie_chow_interpolator]
    type = RhieChowMassFlux
    p_diffusion_kernel = flow_p_diffusion
    pressure = pressure
    rho = rho_mixture
    u = vel_x
    v = vel_y
  []
[]

[Executioner]
  type = SIMPLE
  rhie_chow_user_object = 'ins_rhie_chow_interpolator'

  # Systems
  momentum_systems = 'u_system v_system'
  pressure_system = 'pressure_system'
  active_scalar_systems = 'phi_system'
  momentum_equation_relaxation = 0.8
  active_scalar_equation_relaxation = '0.7'
  pressure_variable_relaxation = 0.3

  # We need to converge the problem to show conservation
  num_iterations = 200
  pressure_absolute_tolerance = 1e-10
  momentum_absolute_tolerance = 1e-10
  active_scalar_absolute_tolerance = '1e-10'
  momentum_petsc_options_iname = '-pc_type -pc_hypre_type'
  momentum_petsc_options_value = 'hypre boomeramg'
  pressure_petsc_options_iname = '-pc_type -pc_hypre_type'
  pressure_petsc_options_value = 'hypre boomeramg'
  active_scalar_petsc_options_iname = '-pc_type -pc_hypre_type'
  active_scalar_petsc_options_value = 'hypre boomeramg'
  momentum_l_abs_tol = 1e-13
  pressure_l_abs_tol = 1e-13
  active_scalar_l_abs_tol = 1e-13
  momentum_l_tol = 0
  pressure_l_tol = 0
  active_scalar_l_tol = 0
  # print_fields = true
  continue_on_max_its = true
[]

[Outputs]
  csv = true
[]

[Postprocessors]
  [Re]
    type = ParsedPostprocessor
    expression = '10.0 * 2 * 1'
  []
  [average_phase2]
    type = ElementAverageValue
    variable = phase_2
  []
  [dp]
    type = PressureDrop
    boundary = 'left right'
    downstream_boundary = right
    pressure = pressure
    upstream_boundary = left
  []
  [max_phase2]
    type = ElementExtremeValue
    variable = phase_2
  []
[]

(modules/navier_stokes/test/tests/finite_volume/ins/channel-flow/linear-segregated/2d-scalar/channel.i)

mu = 2.6
rho = 1.0
advected_interp_method = 'upwind'
k1 = 0.1
k2 = 0.2

[Mesh]
  [mesh]
    type = CartesianMeshGenerator
    dim = 2
    dx = '0.25 0.25'
    dy = '0.2'
    ix = '5 5'
    iy = '5'
    subdomain_id = '0 1'
  []
[]

[Problem]
  linear_sys_names = 'u_system v_system pressure_system s1_system s2_system'
  previous_nl_solution_required = true
[]

[UserObjects]
  [rc]
    type = RhieChowMassFlux
    u = vel_x
    v = vel_y
    pressure = pressure
    rho = ${rho}
    p_diffusion_kernel = p_diffusion
  []
[]

[Variables]
  [vel_x]
    type = MooseLinearVariableFVReal
    initial_condition = 0.5
    solver_sys = u_system
  []
  [vel_y]
    type = MooseLinearVariableFVReal
    solver_sys = v_system
    initial_condition = 0.0
  []
  [pressure]
    type = MooseLinearVariableFVReal
    solver_sys = pressure_system
    initial_condition = 0.2
  []
  [scalar1]
    type = MooseLinearVariableFVReal
    solver_sys = s1_system
    initial_condition = 1.1
  []
  [scalar2]
    type = MooseLinearVariableFVReal
    solver_sys = s2_system
    initial_condition = 3
  []
[]

[LinearFVKernels]
  [u_advection_stress]
    type = LinearWCNSFVMomentumFlux
    variable = vel_x
    advected_interp_method = ${advected_interp_method}
    mu = ${mu}
    u = vel_x
    v = vel_y
    momentum_component = 'x'
    rhie_chow_user_object = 'rc'
    use_nonorthogonal_correction = false
  []
  [v_advection_stress]
    type = LinearWCNSFVMomentumFlux
    variable = vel_y
    advected_interp_method = ${advected_interp_method}
    mu = ${mu}
    u = vel_x
    v = vel_y
    momentum_component = 'y'
    rhie_chow_user_object = 'rc'
    use_nonorthogonal_correction = false
  []
  [u_pressure]
    type = LinearFVMomentumPressure
    variable = vel_x
    pressure = pressure
    momentum_component = 'x'
  []
  [v_pressure]
    type = LinearFVMomentumPressure
    variable = vel_y
    pressure = pressure
    momentum_component = 'y'
  []

  [p_diffusion]
    type = LinearFVAnisotropicDiffusion
    variable = pressure
    diffusion_tensor = Ainv
    use_nonorthogonal_correction = false
  []
  [HbyA_divergence]
    type = LinearFVDivergence
    variable = pressure
    face_flux = HbyA
    force_boundary_execution = true
  []

  [s1_advection]
    type = LinearFVScalarAdvection
    variable = scalar1
    advected_interp_method = ${advected_interp_method}
    rhie_chow_user_object = 'rc'
  []
  [s1_diffusion]
    type = LinearFVDiffusion
    variable = scalar1
    diffusion_coeff = ${k1}
    use_nonorthogonal_correction = false
  []
  [s2_diffusion]
    type = LinearFVScalarAdvection
    variable = scalar2
    advected_interp_method = ${advected_interp_method}
    rhie_chow_user_object = 'rc'
  []
  [s2_conduction]
    type = LinearFVDiffusion
    variable = scalar2
    diffusion_coeff = ${k2}
    use_nonorthogonal_correction = false
  []
[]

[LinearFVBCs]
  [inlet-u]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'left'
    variable = vel_x
    functor = '1.1'
  []
  [inlet-v]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'left'
    variable = vel_y
    functor = '0.0'
  []
  [walls-u]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'top bottom'
    variable = vel_x
    functor = 0.0
  []
  [walls-v]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'top bottom'
    variable = vel_y
    functor = 0.0
  []
  [outlet_p]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'right'
    variable = pressure
    functor = 1.4
  []
  [outlet_u]
    type = LinearFVAdvectionDiffusionOutflowBC
    variable = vel_x
    use_two_term_expansion = false
    boundary = right
  []
  [outlet_v]
    type = LinearFVAdvectionDiffusionOutflowBC
    variable = vel_y
    use_two_term_expansion = false
    boundary = right
  []
  [inlet_wall_scalar1]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    variable = scalar1
    functor = 1
    boundary = 'left'
  []
  [outlet_scalar1]
    type = LinearFVAdvectionDiffusionOutflowBC
    variable = scalar1
    use_two_term_expansion = false
    boundary = right
  []
  [inlet_wall_scalar2]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    variable = scalar2
    functor = 2
    boundary = 'left'
  []
  [outlet_scalar2]
    type = LinearFVAdvectionDiffusionOutflowBC
    variable = scalar2
    use_two_term_expansion = false
    boundary = right
  []
[]

[Executioner]
  type = SIMPLE
  momentum_l_abs_tol = 1e-13
  pressure_l_abs_tol = 1e-13
  passive_scalar_l_abs_tol = 1e-13
  momentum_l_tol = 0
  pressure_l_tol = 0
  passive_scalar_l_tol = 0
  rhie_chow_user_object = 'rc'
  momentum_systems = 'u_system v_system'
  pressure_system = 'pressure_system'
  passive_scalar_systems = 's1_system s2_system'
  momentum_equation_relaxation = 0.8
  passive_scalar_equation_relaxation = '0.9 0.9'
  pressure_variable_relaxation = 0.3
  # We need to converge the problem to show conservation
  num_iterations = 200
  pressure_absolute_tolerance = 1e-10
  momentum_absolute_tolerance = 1e-10
  # The solution being flat, the normalization factor based on fluxes goes to
  # 0. The convergence criteria being multiplied by said factor, we won't do any
  # better than this. For a non-flat solution, use tighter tolerances
  passive_scalar_absolute_tolerance = '1e-2 1e-2'
  momentum_petsc_options_iname = '-pc_type -pc_hypre_type'
  momentum_petsc_options_value = 'hypre boomeramg'
  pressure_petsc_options_iname = '-pc_type -pc_hypre_type'
  pressure_petsc_options_value = 'hypre boomeramg'
  passive_scalar_petsc_options_iname = '-pc_type -pc_hypre_type'
  passive_scalar_petsc_options_value = 'hypre boomeramg'
  print_fields = false
  continue_on_max_its = true
[]

[Outputs]
  exodus = true
  execute_on = timestep_end
  hide = 'pressure vel_x vel_y'
[]

Input Parameters
Input Files