LinearFVEnthalpyVolumetricHeatTransfer

This object adds the volumetric fluid-solid heat transfer term for linear finite volume formulations where the solved variable is the specific enthalpy. This kernel cannot be used when the solved variable is the temperature.

For the current-side equation it contributes

$var element = document.getElementById("moose-equation-522016ec-b592-448e-afd5-95ac7c5d4d0c");katex.render("\\alpha_v\\left(T_{current} - T_{other}\\right),", element, {displayMode:true,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$

where $var element = document.getElementById("moose-equation-df58bde2-4534-46b5-a053-f3ccf8d66004");katex.render("\\alpha_v", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ is the volumetric heat transfer coefficient "h_solid_fluid", and $var element = document.getElementById("moose-equation-ca1771b0-dfc8-44ea-ade4-0b7b1f8045a2");katex.render("T_{current}", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ and $var element = document.getElementById("moose-equation-c59e2941-04f4-474d-ad69-17089607dcf0");katex.render("T_{other}", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ are the temperatures of the phase whose equation this kernel acts on and of the other phase, selected with "is_solid". The current-side temperature is linearized about the latest auxiliary temperature as

$var element = document.getElementById("moose-equation-f5636f1f-9893-400d-9513-c2431b30cf91");katex.render("T_{current}^{k+1} \\approx T_{current}^{k} + \\frac{h_{current}^{k+1} - h_{current}^{k}}{c_p}.", element, {displayMode:true,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$

Here $var element = document.getElementById("moose-equation-24654f32-0244-416d-a15a-0ecd5fc8a75e");katex.render("h_{current}", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ is the specific enthalpy of the current phase, which is the solved variable, $var element = document.getElementById("moose-equation-81eef668-fbce-49b9-b24c-52bb3bab55e9");katex.render("c_p", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ is the specific heat "cp", and superscripts $var element = document.getElementById("moose-equation-0ebb6895-af8a-4aaa-b672-3af9367800d5");katex.render("k", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ and $var element = document.getElementById("moose-equation-3a0fa4bc-d3d6-4fb2-879c-71baef826328");katex.render("k+1", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ denote the previous and the new iterate.

This yields the matrix contribution

$var element = document.getElementById("moose-equation-c9e4a1a2-85b5-44fd-aa07-94cbb223bc22");katex.render("\\frac{\\alpha_v}{c_p},", element, {displayMode:true,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$

and the right-hand side contribution

$var element = document.getElementById("moose-equation-3cc16943-28b6-46f6-b58a-8cb4badcf19c");katex.render("\\alpha_v\\left(T_{other} - T_{current}^{k} + \\frac{h_{current}^{k}}{c_p}\\right).", element, {displayMode:true,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$

If the auxiliary temperature satisfies the constant specific heat relation $var element = document.getElementById("moose-equation-b0340376-9369-498f-bbe7-467e117e7c5d");katex.render("T_{current}^{k}=h_{current}^{k}/c_p", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ , then this reduces exactly to the simpler form $var element = document.getElementById("moose-equation-b79bab23-be8d-40dd-80c2-58b450a71d39");katex.render("\\alpha_v T_{other}", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ .

This kernel is useful for porous-medium fluid and solid enthalpy equations that use auxiliary temperature variables for coupling and boundary data.

Input Parameters

T_fluidFluid temperature.
C++ Type:VariableName
Unit:(no unit assumed)
Controllable:No
Description:Fluid temperature.
T_solidSolid temperature.
C++ Type:VariableName
Unit:(no unit assumed)
Controllable:No
Description:Solid temperature.
cpSpecific heat used to linearize the current-side temperature from the enthalpy variable. 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:Specific heat used to linearize the current-side temperature from the enthalpy variable. A functor is any of the following: a variable, a functor material property, a function, a postprocessor or a number.
h_solid_fluidName of the convective heat transfer coefficient. 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:Name of the convective heat transfer coefficient. A functor is any of the following: a variable, a functor material property, a function, a postprocessor or a number.
is_solidFalseWhether this kernel acts on the solid temperature.
Default:False
C++ Type:bool
Controllable:No
Description:Whether this kernel acts on the solid temperature.
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

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

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_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)
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/pins/channel-flow/linear-segregated/2d-simple-channel-enthalpy/porous-baffle-2d-enthalpy.i)

(modules/navier_stokes/test/tests/finite_volume/pins/channel-flow/linear-segregated/2d-simple-channel-enthalpy/porous-baffle-2d-enthalpy.i)

# Steady conjugate heat transfer from a heated solid to fluid in a 0.5-m porous block.
# The solid fraction scales the 20 MW/m^3 source to 10 MW/m^3. Conservation therefore gives
# u_block_2 = 2, T_fluid_out = 300.59523809524, and h_fluid_out = 1262500.
# For 10 upwind cells, T_fluid_block_2 = 300.32738095238. The local balance gives
# T_solid_block_2 - T_fluid_block_2 = 10e6 / 30000 = 333.33333333333,
# hence T_solid_block_2 = 633.66071428571.

mu = 2e-3
rho = 1000
advected_interp_method = 'upwind'
u_in = 2
forchheimer = 0
bf = '0 0'

cp_fluid = 4200
cp_solid = 500
k_fluid = 0.4
k_solid = 0.2
h_vol = 30000
q_solid = 20000000
T_inlet = 300
T_initial = 300

[FVGradientMethods]
  [jump_aware]
    type = FVPressureJumpGreenGaussGradient
  []
  [velocity_jump_aware]
    type = FVVelocityJumpGreenGaussGradient
  []
  [reconstructed]
    type = FVReconstructedPressureGradient
    base_gradient_method = jump_aware
    gradient_relaxation = 1.0
  []
[]

[Mesh]
  [mesh]
    type = CartesianMeshGenerator
    dim = 2
    dx = '0.5 0.5 0.5'
    dy = '0.5'
    ix = '10 10 10'
    iy = '3'
    subdomain_id = '1 2 3'
  []
  [baffle]
    type = SideSetsBetweenSubdomainsGenerator
    input = mesh
    primary_block = '1'
    paired_block = '2'
    new_boundary = 'baffle'
  []
  [baffle2]
    type = SideSetsBetweenSubdomainsGenerator
    input = baffle
    primary_block = '2'
    paired_block = '3'
    new_boundary = 'baffle2'
  []
  [split_top_bottom]
    type = BreakBoundaryOnSubdomainGenerator
    input = baffle2
    boundaries = 'top bottom'
  []
  [delete]
    type = BoundaryDeletionGenerator
    boundary_names = 'top bottom'
    input = split_top_bottom
  []
[]

[FVInterpolationMethods]
  [upwind]
    type = FVAdvectedUpwind
  []
[]

[Problem]
  linear_sys_names = 'u_system v_system pressure_system energy_system solid_energy_system'
  previous_nl_solution_required = true
[]

[UserObjects]
  [pressure_jump]
    type = BernoulliFormLossPressureJump
    boundary = 'baffle baffle2'
    porosity = porosity
    density = ${rho}
    form_loss = ${bf}
    reference_velocity_side = 'lower_porosity higher_porosity'
  []
  [rc]
    type = PorousRhieChowMassFlux
    u = superficial_u
    v = superficial_v
    pressure = pressure
    rho = ${rho}
    porosity = porosity
    p_diffusion_kernel = p_diffusion
    pressure_jump_models = pressure_jump
    pressure_jump_relaxation = 0.1
  []
[]

[Variables]
  [superficial_u]
    type = MooseLinearVariableFVReal
    solver_sys = u_system
    initial_condition = ${u_in}
    gradient_method = velocity_jump_aware
  []
  [superficial_v]
    type = MooseLinearVariableFVReal
    solver_sys = v_system
    initial_condition = 0.0
    gradient_method = velocity_jump_aware
  []
  [pressure]
    type = MooseLinearVariableFVReal
    solver_sys = pressure_system
    initial_condition = 0.0
    gradient_method = jump_aware
  []
  [h_fluid]
    type = MooseLinearVariableFVReal
    solver_sys = energy_system
    initial_condition = '${fparse cp_fluid * T_initial}'
  []
  [T_solid]
    type = MooseLinearVariableFVReal
    solver_sys = solid_energy_system
    initial_condition = ${T_initial}
    block = 2
  []
[]

[LinearFVKernels]
  [u_advection]
    type = LinearPWCNSFVMomentumFlux
    variable = superficial_u
    advected_interp_method_name = ${advected_interp_method}
    mu = ${mu}
    u = superficial_u
    v = superficial_v
    momentum_component = 'x'
    rhie_chow_user_object = rc
    use_nonorthogonal_correction = false
  []
  [v_advection]
    type = LinearPWCNSFVMomentumFlux
    variable = superficial_v
    advected_interp_method_name = ${advected_interp_method}
    mu = ${mu}
    u = superficial_u
    v = superficial_v
    momentum_component = 'y'
    rhie_chow_user_object = rc
    use_nonorthogonal_correction = false
  []
  [u_pressure]
    type = LinearPWCNSFVMomentumPressure
    variable = superficial_u
    momentum_component = 'x'
    porosity = porosity
    pressure = pressure
    gradient_method = reconstructed
  []
  [v_pressure]
    type = LinearPWCNSFVMomentumPressure
    variable = superficial_v
    momentum_component = 'y'
    porosity = porosity
    pressure = pressure
    gradient_method = reconstructed
  []
  [u_friction]
    type = LinearFVMomentumFriction
    variable = superficial_u
    Forchheimer_name = forch
    porosity = porosity
    rho = ${rho}
    u = superficial_u
    v = superficial_v
    momentum_component = 'x'
    block = 2
  []
  [v_friction]
    type = LinearFVMomentumFriction
    variable = superficial_v
    Forchheimer_name = forch
    porosity = porosity
    rho = ${rho}
    u = superficial_u
    v = superficial_v
    momentum_component = 'y'
    block = 2
  []
  [p_diffusion]
    type = LinearFVPressureCorrectionDiffusionJump
    variable = pressure
    rhie_chow_user_object = rc
    use_nonorthogonal_correction = false
  []
  [HbyA_divergence]
    type = LinearFVDivergence
    variable = pressure
    face_flux = HbyA
    force_boundary_execution = true
  []

  [fluid_advection]
    type = LinearFVEnergyAdvection
    variable = h_fluid
    advected_quantity = enthalpy
    advected_interp_method = ${advected_interp_method}
    rhie_chow_user_object = rc
  []
  [fluid_diffusion]
    type = LinearFVDiffusion
    variable = h_fluid
    diffusion_coeff = kappa_fluid
    use_nonorthogonal_correction = false
  []
  [fluid_exchange]
    type = LinearFVEnthalpyVolumetricHeatTransfer
    variable = h_fluid
    h_solid_fluid = h_vol
    cp = cp_fluid
    T_fluid = T_fluid
    T_solid = T_solid
    is_solid = false
    block = 2
  []
  [fluid_source]
    type = LinearFVSource
    variable = h_fluid
    source_density = q_fluid_scaled
  []

  [solid_diffusion]
    type = LinearFVDiffusion
    variable = T_solid
    diffusion_coeff = ${k_solid}
    use_nonorthogonal_correction = false
    block = 2
  []
  [solid_exchange]
    type = LinearFVEnthalpyVolumetricHeatTransfer
    variable = T_solid
    h_solid_fluid = h_vol
    cp = 1.0
    T_fluid = T_fluid
    T_solid = T_solid
    is_solid = true
    block = 2
  []
  [solid_source]
    type = LinearFVSource
    variable = T_solid
    source_density = q_solid_scaled
    block = 2
  []
[]

[LinearFVBCs]
  [left_u]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = left
    variable = superficial_u
    functor = ${u_in}
  []
  [outlet_u]
    type = LinearFVAdvectionDiffusionOutflowBC
    boundary = right
    variable = superficial_u
    use_two_term_expansion = false
  []

  [left_v]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = left
    variable = superficial_v
    functor = 0.0
  []
  [outlet_v]
    type = LinearFVAdvectionDiffusionOutflowBC
    boundary = right
    variable = superficial_v
    use_two_term_expansion = false
  []

  [symmetry-u]
    type = LinearFVVelocitySymmetryBC
    boundary = 'top_to_1 top_to_3 bottom_to_1 bottom_to_3 top_to_2 bottom_to_2'
    variable = superficial_u
    u = superficial_u
    v = superficial_v
    momentum_component = x
  []
  [symmetry-v]
    type = LinearFVVelocitySymmetryBC
    boundary = 'top_to_1 top_to_3 bottom_to_1 bottom_to_3 top_to_2 bottom_to_2'
    variable = superficial_v
    u = superficial_u
    v = superficial_v
    momentum_component = y
  []

  [pressure-extrapolation]
    type = LinearFVPressureFluxBC
    boundary = 'bottom_to_1 bottom_to_2 bottom_to_3 top_to_1 top_to_2 top_to_3'
    variable = pressure
    HbyA_flux = HbyA
    Ainv = Ainv
    rho = ${rho}
    u = superficial_u
    v = superficial_v
  []

  [outlet_p]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = right
    variable = pressure
    functor = 0.0
  []

  [left_T_fluid]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = left
    variable = T_fluid
    functor = ${T_inlet}
  []
  [left_h_fluid]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = left
    variable = h_fluid
    functor = h_from_p_T
  []
  [walls_h_fluid]
    type = LinearFVAdvectionDiffusionFunctorNeumannBC
    boundary = 'top_to_1 top_to_2 top_to_3 bottom_to_1 bottom_to_2 bottom_to_3'
    variable = h_fluid
    functor = 0.0
    diffusion_coeff = kappa_fluid
  []
  [outlet_h_fluid]
    type = LinearFVAdvectionDiffusionOutflowBC
    boundary = right
    variable = h_fluid
    use_two_term_expansion = false
  []

  [solid_zero_flux]
    type = LinearFVAdvectionDiffusionFunctorNeumannBC
    boundary = 'baffle baffle2 top_to_2 bottom_to_2'
    variable = T_solid
    functor = 0.0
    diffusion_coeff = kappa_solid
  []
[]

[FunctorMaterials]
  [forch]
    type = GenericVectorFunctorMaterial
    prop_names = forch
    prop_values = '${forchheimer} ${forchheimer} ${forchheimer}'
  []
  [porosity]
    type = PiecewiseByBlockFunctorMaterial
    prop_name = porosity
    subdomain_to_prop_value = '1 1.0 2 0.5 3 1.0'
  []
  [fluid_constants]
    type = GenericFunctorMaterial
    prop_names = 'cp_fluid kappa_fluid h_vol q_fluid_scaled'
    prop_values = '${cp_fluid} ${fparse k_fluid/cp_fluid} ${h_vol} 0'
  []
  [solid_constants]
    type = GenericFunctorMaterial
    prop_names = 'cp_solid kappa_solid'
    prop_values = '${cp_solid} ${fparse k_solid/cp_solid}'
  []
  [q_solid]
    type = GenericFunctorMaterial
    prop_names = 'q_solid'
    prop_values = ${q_solid}
    block = 2
  []
  [q_solid_scaled]
    type = ParsedFunctorMaterial
    property_name = q_solid_scaled
    functor_names = 'porosity q_solid'
    expression = '(1 - porosity) * q_solid'
    block = 2
  []
  [fluid_enthalpy_material]
    type = LinearFVEnthalpyFunctorMaterial
    pressure = pressure
    T_fluid = T_fluid
    h = h_fluid
    h_from_p_T_functor = h_from_p_T_functor
    T_from_p_h_functor = T_from_p_h_functor
  []
  [h_from_p_T_functor]
    type = ParsedFunctorMaterial
    property_name = h_from_p_T_functor
    functor_names = 'T_fluid'
    expression = '${cp_fluid} * T_fluid'
  []
  [T_from_p_h_functor]
    type = ParsedFunctorMaterial
    property_name = T_from_p_h_functor
    functor_names = 'h_fluid'
    expression = 'h_fluid / ${cp_fluid}'
  []
[]

[Postprocessors]
  [u_block_2]
    type = ElementAverageValue
    variable = superficial_u
    block = 2
  []
  [T_fluid_out]
    type = SideAverageValue
    variable = T_fluid
    boundary = right
  []
  [T_fluid_block_2]
    type = ElementAverageValue
    variable = T_fluid
    block = 2
  []
  [T_solid_block_2]
    type = ElementAverageValue
    variable = T_solid
    block = 2
  []
  [h_fluid_out]
    type = SideAverageValue
    variable = h_fluid
    boundary = right
  []
[]

[AuxVariables]
  [porosity_aux]
    type = MooseLinearVariableFVReal
  []
  [T_fluid]
    type = MooseLinearVariableFVReal
    initial_condition = ${T_initial}
  []
[]

[AuxKernels]
  [por]
    type = FunctorAux
    variable = porosity_aux
    functor = porosity
    execute_on = 'NONLINEAR'
  []
  [fluid_temperature]
    type = FunctorAux
    variable = T_fluid
    functor = T_from_p_h
    execute_on = 'NONLINEAR'
  []
[]

[VectorPostprocessors]
  # Sample each x-cell once at its center.
  [centerline]
    type = LineValueSampler
    variable = 'superficial_u T_fluid T_solid'
    start_point = '0.0119047619047619 0.25 0'
    end_point = '1.4880952380952381 0.25 0'
    num_points = 30
    sort_by = x
  []
[]

[Executioner]
  type = SIMPLE
  momentum_l_abs_tol = 1e-14
  pressure_l_abs_tol = 1e-14
  energy_l_abs_tol = 1e-14
  solid_energy_l_abs_tol = 1e-14
  momentum_l_tol = 0
  pressure_l_tol = 0
  energy_l_tol = 0
  solid_energy_l_tol = 0
  rhie_chow_user_object = rc
  momentum_systems = 'u_system v_system'
  pressure_system = pressure_system
  energy_system = energy_system
  solid_energy_system = solid_energy_system
  momentum_equation_relaxation = 0.2
  pressure_variable_relaxation = 0.1
  energy_equation_relaxation = 0.8
  num_iterations = 1000
  # These outer tolerances stop once the velocity and zero-pressure fields have stabilized to
  # substantially below the accuracy exercised by the temperature and velocity profile checks.
  pressure_absolute_tolerance = 1e-6
  momentum_absolute_tolerance = 1e-2
  energy_absolute_tolerance = 1e-8
  solid_energy_absolute_tolerance = 1e-8
  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'
  energy_petsc_options_iname = '-pc_type -pc_hypre_type'
  energy_petsc_options_value = 'hypre boomeramg'
  solid_energy_petsc_options_iname = '-pc_type -pc_hypre_type'
  solid_energy_petsc_options_value = 'hypre boomeramg'
[]

[Outputs]
  csv = true
  execute_on = FINAL
[]

Input Parameters
Input Files