LinearFVEnthalpyFunctorMaterial

This FunctorMaterial class is needed when the user wants to solve for the enthalpy conservation for the linear finite-volume implementation of the incompressible/weakly-compressible Navier-Stokes equations.

This material class defines the functors to convert from specific enthalpy and pressure to temperature ('T_from_p_h') and to convert from temperature and pressure to specific enthalpy ('h_from_p_T').

When solving the enthalpy conservation equation and obtaining the specific enthalpy ( $var element = document.getElementById("moose-equation-7cce9ae1-bb2c-4ebe-81b3-7ceac329028c");katex.render("h", element, {displayMode:false,throwOnError:false});$ ) as the solution, two functors are required. The 'T_from_p_h' functor computes the temperature field, which is then used to evaluate temperature-dependent thermophysical properties. The 'h_from_p_T' functor is primarily utilized for setting boundary conditions where the temperature is specified.

The specific enthalpy is defined as:

$var element = document.getElementById("moose-equation-d65201ae-d4e1-4066-a801-b54e7420a60e");katex.render(" h(T) = \\int_{T_{ref}}^{T} c_p(p, T')dT' + h_{ref},", element, {displayMode:true,throwOnError:false});$

where

$var element = document.getElementById("moose-equation-bd629fd5-28a3-4a11-b286-004b68a7c65c");katex.render("c_p(p, T)", element, {displayMode:false,throwOnError:false});$ is the pressure and temperature-dependent specific heat
$var element = document.getElementById("moose-equation-ec523887-3dc8-4a74-9606-1547a5f8ee78");katex.render("T_{ref}", element, {displayMode:false,throwOnError:false});$ is a reference temperature where the reference enthalpy $var element = document.getElementById("moose-equation-9789e60a-cd9a-4b97-ac04-beccdad5d687");katex.render("h_{ref}", element, {displayMode:false,throwOnError:false});$ is defined

Example input syntax 1: Fluid Properties

In this input, a LinearFVEnthalpyFunctorMaterial is defined to solve for a 1D heated channel using lead fluid properties with a fixed mass flux.

The FluidProperties object for lead is defined in

[FluidProperties<<<{"href": "../../syntax/FluidProperties/index.html"}>>>]
  [lead]
    type = LeadFluidProperties<<<{"description": "Fluid properties for Lead", "href": "../fluidproperties/LeadFluidProperties.html"}>>>
  []
[]

Then, the LinearFVEnthalpyFunctorMaterial is defined taking the FluidProperties object as an input, which already contains the 'h_from_p_T' and 'T_from_p_h' functors defined.

[FunctorMaterials<<<{"href": "../../syntax/FunctorMaterials/index.html"}>>>]
  [enthalpy_material]
    type = LinearFVEnthalpyFunctorMaterial<<<{"description": "Creates functors for conversions between specific enthalpy and temperature", "href": "LinearFVEnthalpyFunctorMaterial.html"}>>>
    pressure<<<{"description": "Pressure. A functor is any of the following: a variable, a functor material property, a function, a postprocessor or a number."}>>> = ${p_ref}
    T_fluid<<<{"description": "Fluid temperature. A functor is any of the following: a variable, a functor material property, a function, a postprocessor or a number."}>>> = T
    h<<<{"description": "Specific Enthalpy. A functor is any of the following: a variable, a functor material property, a function, a postprocessor or a number."}>>> = h
    fp<<<{"description": "Fluid properties userobject"}>>> = lead
  []
[]

Example input syntax 2: User-Defined Properties

In this input, a LinearFVEnthalpyFunctorMaterial is defined to solve for a 1D heated channel using FLiNaK properties with a fixed mass flux, defined by the user.

[FunctorMaterials<<<{"href": "../../syntax/FunctorMaterials/index.html"}>>>]
  [enthalpy_material]
    type = LinearFVEnthalpyFunctorMaterial<<<{"description": "Creates functors for conversions between specific enthalpy and temperature", "href": "LinearFVEnthalpyFunctorMaterial.html"}>>>
    pressure<<<{"description": "Pressure. A functor is any of the following: a variable, a functor material property, a function, a postprocessor or a number."}>>> = ${p_ref}
    T_fluid<<<{"description": "Fluid temperature. A functor is any of the following: a variable, a functor material property, a function, a postprocessor or a number."}>>> = T
    h<<<{"description": "Specific Enthalpy. A functor is any of the following: a variable, a functor material property, a function, a postprocessor or a number."}>>> = h
    h_from_p_T_functor<<<{"description": "User specified enthalpy from temperature functor. A functor is any of the following: a variable, a functor material property, a function, a postprocessor or a number."}>>> = h_from_p_T_functor
    T_from_p_h_functor<<<{"description": "User specified temperature from enthalpy functor. A functor is any of the following: a variable, a functor material property, a function, a postprocessor or a number."}>>> = T_from_p_h_functor
  []
[]

This functor material takes the user-defined 'h_from_p_T' and 'T_from_p_h' functors as inputs. The functors are defined in

[FunctorMaterials<<<{"href": "../../syntax/FunctorMaterials/index.html"}>>>]
  [h_from_p_T_functor]
    type = ParsedFunctorMaterial<<<{"description": "Computes a functor material from a parsed expression of other functors.", "href": "ParsedFunctorMaterial.html"}>>>
    property_name<<<{"description": "Name to give the new functor material property"}>>> = 'h_from_p_T_functor'
    functor_names<<<{"description": "Functors to use in the parsed expression"}>>> = 'T'
    expression<<<{"description": "Expression to parse for the new functor material"}>>> = '${A_cp}*T+${B_cp}/2*(T^2)'
  []
[]

[FunctorMaterials<<<{"href": "../../syntax/FunctorMaterials/index.html"}>>>]
  [T_from_p_h_functor]
    type = ParsedFunctorMaterial<<<{"description": "Computes a functor material from a parsed expression of other functors.", "href": "ParsedFunctorMaterial.html"}>>>
    property_name<<<{"description": "Name to give the new functor material property"}>>> = 'T_from_p_h_functor'
    functor_names<<<{"description": "Functors to use in the parsed expression"}>>> = 'h'
    expression<<<{"description": "Expression to parse for the new functor material"}>>> = '(-${A_cp}+sqrt(${A_cp}^2+2*h*${B_cp}))/${B_cp}'
  []
[]

for the linear specific heat:

[FunctorMaterials<<<{"href": "../../syntax/FunctorMaterials/index.html"}>>>]
  [cp]
    type = ADParsedFunctorMaterial<<<{"description": "Computes a functor material from a parsed expression of other functors.", "href": "ParsedFunctorMaterial.html"}>>>
    property_name<<<{"description": "Name to give the new functor material property"}>>> = 'cp'
    functor_names<<<{"description": "Functors to use in the parsed expression"}>>> = 'T'
    expression<<<{"description": "Expression to parse for the new functor material"}>>> = '${A_cp}+${B_cp}*T'
  []
[]

warning

If using user-defined properties, it is the responsibility of the user to update these properties often enough. For example auxiliary variable properties would only be updated at the end of every time step by default, which would introduce a lag.

Input Parameters

T_fluidFluid temperature. 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:Fluid temperature. A functor is any of the following: a variable, a functor material property, a function, a postprocessor or a number.
hSpecific Enthalpy. 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 Enthalpy. A functor is any of the following: a variable, a functor material property, a function, a postprocessor or a number.
pressurePressure. 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:Pressure. A functor is any of the following: a variable, a functor material property, a function, a postprocessor or a number.

Required Parameters

T_from_p_h_functorUser specified temperature from enthalpy functor. 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:User specified temperature from enthalpy functor. A functor is any of the following: a variable, a functor material property, a function, a postprocessor or a number.
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
declare_suffixAn optional suffix parameter that can be appended to any declared properties. The suffix will be prepended with a '_' character.
C++ Type:MaterialPropertyName
Unit:(no unit assumed)
Controllable:No
Description:An optional suffix parameter that can be appended to any declared properties. The suffix will be prepended with a '_' character.
execute_onALWAYSThe list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html.
Default:ALWAYS
C++ Type:ExecFlagEnum
Options:XFEM_MARK, NONE, INITIAL, LINEAR, LINEAR_CONVERGENCE, NONLINEAR, NONLINEAR_CONVERGENCE, POSTCHECK, TIMESTEP_END, TIMESTEP_BEGIN, MULTIAPP_FIXED_POINT_END, MULTIAPP_FIXED_POINT_BEGIN, MULTIAPP_FIXED_POINT_CONVERGENCE, FINAL, CUSTOM, ALWAYS
Controllable:No
Description:The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html.
fpFluid properties userobject
C++ Type:UserObjectName
Controllable:No
Description:Fluid properties userobject
h_from_p_T_functorUser specified enthalpy from temperature functor. 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:User specified enthalpy from temperature functor. A functor is any of the following: a variable, a functor material property, a function, a postprocessor or a number.

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

(moose/modules/navier_stokes/test/tests/finite_volume/wcns/enthalpy_equation/1d_test_h_fp.i)

L = 30
nx = 600
bulk_u = 0.01
p_ref = 101325.0
T_in = 860.
q_source = 20000.
advected_interp_method = 'upwind'

[Mesh]
  [gmg]
    type = GeneratedMeshGenerator
    dim = 1
    xmin = 0
    xmax = ${L}
    nx = ${nx}
  []
  allow_renumbering = false
[]

[GlobalParams]
  rhie_chow_user_object = 'rc'
  advected_interp_method = ${advected_interp_method}
  u = vel_x
[]

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

[UserObjects]
  [rc]
    type = RhieChowMassFlux
    u = vel_x
    pressure = pressure
    rho = 'rho'
    p_diffusion_kernel = p_diffusion
  []
[]

[Variables]
  [vel_x]
    type = MooseLinearVariableFVReal
    solver_sys = u_system
    initial_condition = ${bulk_u}
  []
  [pressure]
    type = MooseLinearVariableFVReal
    solver_sys = pressure_system
    initial_condition = ${p_ref}
  []
  [h]
    type = MooseLinearVariableFVReal
    solver_sys = energy_system
    initial_condition = ${fparse 860.*240.}
  []
[]

[AuxVariables]
  [rho_var]
    type = MooseLinearVariableFVReal
  []
  [cp_var]
    type = MooseLinearVariableFVReal
  []
  [mu_var]
    type = MooseLinearVariableFVReal
  []
  [k_var]
    type = MooseLinearVariableFVReal
  []
  [alpha_var]
    type = MooseLinearVariableFVReal
  []
  [T]
    type = MooseLinearVariableFVReal
    initial_condition = ${T_in}
  []
  [h_aux]
    type = MooseLinearVariableFVReal
  []
[]

[LinearFVKernels]

  [u_advection_stress]
    type = LinearWCNSFVMomentumFlux
    variable = vel_x
    mu = 'mu'
    momentum_component = 'x'
    use_nonorthogonal_correction = false
  []
  [u_pressure]
    type = LinearFVMomentumPressure
    variable = vel_x
    pressure = pressure
    momentum_component = 'x'
  []

  [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
  []

  [temp_advection]
    type = LinearFVEnergyAdvection
    variable = h
  []
  [source]
    type = LinearFVSource
    variable = h
    source_density = source_func
  []
[]

[LinearFVBCs]
  [inlet_u]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'left'
    variable = vel_x
    functor = ${bulk_u}
  []
  [inlet_h]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    variable = h
    boundary = 'left'
    functor = 'h_from_p_T'
  []
  [inlet_T]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    variable = T
    boundary = 'left'
    functor = ${T_in}
  []

  [outlet_p]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'right'
    variable = pressure
    functor = ${p_ref}
  []
  [outlet_h]
    type = LinearFVAdvectionDiffusionOutflowBC
    variable = h
    use_two_term_expansion = false
    boundary = 'right'
  []
  [outlet_u]
    type = LinearFVAdvectionDiffusionOutflowBC
    variable = vel_x
    use_two_term_expansion = false
    boundary = 'right'
  []
[]

[FluidProperties]
  [lead]
    type = LeadFluidProperties
  []
[]

[FunctorMaterials]
  [enthalpy_material]
    type = LinearFVEnthalpyFunctorMaterial
    pressure = ${p_ref}
    T_fluid = T
    h = h
    fp = lead
  []
  [fluid_props_to_mat_props]
    type = GeneralFunctorFluidProps
    fp = lead
    pressure = ${p_ref}
    T_fluid = 'T'
    speed = 1
    porosity = 1
    characteristic_length = 1
  []
  [source_func]
    type = ADParsedFunctorMaterial
    property_name = source_func
    functor_names = 'rho'
    expression = ${q_source}
  []
[]

[AuxKernels]
  [rho_out]
    type = FunctorAux
    functor = 'rho'
    variable = 'rho_var'
    execute_on = 'NONLINEAR'
  []
  [cp_out]
    type = FunctorAux
    functor = 'cp'
    variable = 'cp_var'
    execute_on = 'NONLINEAR'
  []
  [mu_out]
    type = FunctorAux
    functor = 'mu'
    variable = 'mu_var'
    execute_on = 'NONLINEAR'
  []
  [k_out]
    type = FunctorAux
    functor = 'k'
    variable = 'k_var'
    execute_on = 'NONLINEAR'
  []
  [T_from_h_functor_aux]
    type = FunctorAux
    functor = 'T_from_p_h'
    variable = 'T'
    execute_on = 'NONLINEAR'
  []
  [h_from_T_functor_aux]
    type = FunctorAux
    functor = 'h_from_p_T'
    variable = 'h_aux'
    execute_on = 'NONLINEAR'
  []
[]

[Postprocessors]
  [T_out_sim]
    type = ElementalVariableValue
    variable = T
    elementid = ${fparse nx-1}
  []
[]

[Executioner]
  type = SIMPLE
  momentum_l_abs_tol = 1e-12
  pressure_l_abs_tol = 1e-12
  energy_l_abs_tol = 1e-12
  momentum_l_tol = 0
  pressure_l_tol = 0
  energy_l_tol = 0
  rhie_chow_user_object = 'rc'
  momentum_systems = 'u_system'
  pressure_system = 'pressure_system'
  energy_system = 'energy_system'
  momentum_equation_relaxation = 0.7
  pressure_variable_relaxation = 0.3
  energy_equation_relaxation = 0.95
  num_iterations = 100
  pressure_absolute_tolerance = 1e-8
  momentum_absolute_tolerance = 1e-8
  energy_absolute_tolerance = 1e-6
  print_fields = false
  momentum_l_max_its = 200

  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'
  continue_on_max_its = true
[]

[Outputs]
  [out]
    type = CSV
  []
[]

(moose/modules/navier_stokes/test/tests/finite_volume/wcns/enthalpy_equation/1d_test_h_fp.i)

L = 30
nx = 600
bulk_u = 0.01
p_ref = 101325.0
T_in = 860.
q_source = 20000.
advected_interp_method = 'upwind'

[Mesh]
  [gmg]
    type = GeneratedMeshGenerator
    dim = 1
    xmin = 0
    xmax = ${L}
    nx = ${nx}
  []
  allow_renumbering = false
[]

[GlobalParams]
  rhie_chow_user_object = 'rc'
  advected_interp_method = ${advected_interp_method}
  u = vel_x
[]

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

[UserObjects]
  [rc]
    type = RhieChowMassFlux
    u = vel_x
    pressure = pressure
    rho = 'rho'
    p_diffusion_kernel = p_diffusion
  []
[]

[Variables]
  [vel_x]
    type = MooseLinearVariableFVReal
    solver_sys = u_system
    initial_condition = ${bulk_u}
  []
  [pressure]
    type = MooseLinearVariableFVReal
    solver_sys = pressure_system
    initial_condition = ${p_ref}
  []
  [h]
    type = MooseLinearVariableFVReal
    solver_sys = energy_system
    initial_condition = ${fparse 860.*240.}
  []
[]

[AuxVariables]
  [rho_var]
    type = MooseLinearVariableFVReal
  []
  [cp_var]
    type = MooseLinearVariableFVReal
  []
  [mu_var]
    type = MooseLinearVariableFVReal
  []
  [k_var]
    type = MooseLinearVariableFVReal
  []
  [alpha_var]
    type = MooseLinearVariableFVReal
  []
  [T]
    type = MooseLinearVariableFVReal
    initial_condition = ${T_in}
  []
  [h_aux]
    type = MooseLinearVariableFVReal
  []
[]

[LinearFVKernels]

  [u_advection_stress]
    type = LinearWCNSFVMomentumFlux
    variable = vel_x
    mu = 'mu'
    momentum_component = 'x'
    use_nonorthogonal_correction = false
  []
  [u_pressure]
    type = LinearFVMomentumPressure
    variable = vel_x
    pressure = pressure
    momentum_component = 'x'
  []

  [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
  []

  [temp_advection]
    type = LinearFVEnergyAdvection
    variable = h
  []
  [source]
    type = LinearFVSource
    variable = h
    source_density = source_func
  []
[]

[LinearFVBCs]
  [inlet_u]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'left'
    variable = vel_x
    functor = ${bulk_u}
  []
  [inlet_h]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    variable = h
    boundary = 'left'
    functor = 'h_from_p_T'
  []
  [inlet_T]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    variable = T
    boundary = 'left'
    functor = ${T_in}
  []

  [outlet_p]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'right'
    variable = pressure
    functor = ${p_ref}
  []
  [outlet_h]
    type = LinearFVAdvectionDiffusionOutflowBC
    variable = h
    use_two_term_expansion = false
    boundary = 'right'
  []
  [outlet_u]
    type = LinearFVAdvectionDiffusionOutflowBC
    variable = vel_x
    use_two_term_expansion = false
    boundary = 'right'
  []
[]

[FluidProperties]
  [lead]
    type = LeadFluidProperties
  []
[]

[FunctorMaterials]
  [enthalpy_material]
    type = LinearFVEnthalpyFunctorMaterial
    pressure = ${p_ref}
    T_fluid = T
    h = h
    fp = lead
  []
  [fluid_props_to_mat_props]
    type = GeneralFunctorFluidProps
    fp = lead
    pressure = ${p_ref}
    T_fluid = 'T'
    speed = 1
    porosity = 1
    characteristic_length = 1
  []
  [source_func]
    type = ADParsedFunctorMaterial
    property_name = source_func
    functor_names = 'rho'
    expression = ${q_source}
  []
[]

[AuxKernels]
  [rho_out]
    type = FunctorAux
    functor = 'rho'
    variable = 'rho_var'
    execute_on = 'NONLINEAR'
  []
  [cp_out]
    type = FunctorAux
    functor = 'cp'
    variable = 'cp_var'
    execute_on = 'NONLINEAR'
  []
  [mu_out]
    type = FunctorAux
    functor = 'mu'
    variable = 'mu_var'
    execute_on = 'NONLINEAR'
  []
  [k_out]
    type = FunctorAux
    functor = 'k'
    variable = 'k_var'
    execute_on = 'NONLINEAR'
  []
  [T_from_h_functor_aux]
    type = FunctorAux
    functor = 'T_from_p_h'
    variable = 'T'
    execute_on = 'NONLINEAR'
  []
  [h_from_T_functor_aux]
    type = FunctorAux
    functor = 'h_from_p_T'
    variable = 'h_aux'
    execute_on = 'NONLINEAR'
  []
[]

[Postprocessors]
  [T_out_sim]
    type = ElementalVariableValue
    variable = T
    elementid = ${fparse nx-1}
  []
[]

[Executioner]
  type = SIMPLE
  momentum_l_abs_tol = 1e-12
  pressure_l_abs_tol = 1e-12
  energy_l_abs_tol = 1e-12
  momentum_l_tol = 0
  pressure_l_tol = 0
  energy_l_tol = 0
  rhie_chow_user_object = 'rc'
  momentum_systems = 'u_system'
  pressure_system = 'pressure_system'
  energy_system = 'energy_system'
  momentum_equation_relaxation = 0.7
  pressure_variable_relaxation = 0.3
  energy_equation_relaxation = 0.95
  num_iterations = 100
  pressure_absolute_tolerance = 1e-8
  momentum_absolute_tolerance = 1e-8
  energy_absolute_tolerance = 1e-6
  print_fields = false
  momentum_l_max_its = 200

  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'
  continue_on_max_its = true
[]

[Outputs]
  [out]
    type = CSV
  []
[]

(moose/modules/navier_stokes/test/tests/finite_volume/wcns/enthalpy_equation/1d_test_h.i)

L = 30
nx = 600
bulk_u = 0.01
q_source = 50000.
A_cp = 976.78
B_cp = 1.0634
T_in = 860.
p_ref = 101325.0
rho = 2000.
advected_interp_method = 'upwind'

[Mesh]
  [gmg]
    type = GeneratedMeshGenerator
    dim = 1
    xmin = 0
    xmax = ${L}
    nx = ${nx}
  []
  allow_renumbering = false
[]

[GlobalParams]
  rhie_chow_user_object = 'rc'
  advected_interp_method = ${advected_interp_method}
  u = vel_x
[]

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

[UserObjects]
  [rc]
    type = RhieChowMassFlux
    u = vel_x
    pressure = pressure
    rho = 'rho'
    p_diffusion_kernel = p_diffusion
  []
[]

[Variables]
  [vel_x]
    type = MooseLinearVariableFVReal
    solver_sys = u_system
    initial_condition = ${bulk_u}
  []
  [pressure]
    type = MooseLinearVariableFVReal
    solver_sys = pressure_system
    initial_condition = ${p_ref}
  []
  [h]
    type = MooseLinearVariableFVReal
    solver_sys = energy_system
    initial_condition = ${fparse 860.*1900.}
  []
[]

[AuxVariables]
  [rho_var]
    type = MooseLinearVariableFVReal
  []
  [cp_var]
    type = MooseLinearVariableFVReal
  []
  [mu_var]
    type = MooseLinearVariableFVReal
  []
  [k_var]
    type = MooseLinearVariableFVReal
  []
  [alpha_var]
    type = MooseLinearVariableFVReal
  []
  [T]
    type = MooseLinearVariableFVReal
    initial_condition = 860.
  []
  [h_aux]
    type = MooseLinearVariableFVReal
  []
[]

[LinearFVKernels]

  [u_advection_stress]
    type = LinearWCNSFVMomentumFlux
    variable = vel_x
    mu = 'mu'
    momentum_component = 'x'
    use_nonorthogonal_correction = false
  []
  [u_pressure]
    type = LinearFVMomentumPressure
    variable = vel_x
    pressure = pressure
    momentum_component = 'x'
  []

  [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
  []

  [temp_advection]
    type = LinearFVEnergyAdvection
    variable = h
  []
  [source]
    type = LinearFVSource
    variable = h
    source_density = source_func
  []
[]

[LinearFVBCs]
  [inlet_u]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'left'
    variable = vel_x
    functor = ${bulk_u} #${bulk_u} #'fully_developed_velocity'
  []
  [inlet_h]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    variable = h
    boundary = 'left'
    functor = 'h_from_p_T'
  []
  [inlet_T]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    variable = T
    boundary = 'left'
    functor = ${T_in}
  []

  [outlet_p]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'right'
    variable = pressure
    functor = ${p_ref}
  []
  [outlet_h]
    type = LinearFVAdvectionDiffusionOutflowBC
    variable = h
    use_two_term_expansion = false
    boundary = 'right'
  []
  [outlet_u]
    type = LinearFVAdvectionDiffusionOutflowBC
    variable = vel_x
    use_two_term_expansion = false
    boundary = 'right'
  []
[]

[Functions]
  [source_func]
    type = ParsedFunction
    expression = ${q_source}
  []
  [T_analytical]
    type = ParsedFunction
    expression = ${fparse (-A_cp+sqrt(A_cp^2-2*B_cp*(-q_source/rho/bulk_u*L-A_cp*T_in-B_cp/2*T_in*T_in)))/B_cp}
  []
[]

[FunctorMaterials]
  [enthalpy_material]
    type = LinearFVEnthalpyFunctorMaterial
    pressure = ${p_ref}
    T_fluid = T
    h = h
    h_from_p_T_functor = h_from_p_T_functor
    T_from_p_h_functor = T_from_p_h_functor
  []
  [h_from_p_T_functor]
    type = ParsedFunctorMaterial
    property_name = 'h_from_p_T_functor'
    functor_names = 'T'
    expression = '${A_cp}*T+${B_cp}/2*(T^2)'
  []
  [T_from_p_h_functor]
    type = ParsedFunctorMaterial
    property_name = 'T_from_p_h_functor'
    functor_names = 'h'
    expression = '(-${A_cp}+sqrt(${A_cp}^2+2*h*${B_cp}))/${B_cp}'
  []
  [rho]
    type = ADParsedFunctorMaterial
    property_name = 'rho'
    functor_names = 'T'
    expression = ${rho}
  []
  [cp]
    type = ADParsedFunctorMaterial
    property_name = 'cp'
    functor_names = 'T'
    expression = '${A_cp}+${B_cp}*T'
  []
  [mu]
    type = ADParsedFunctorMaterial
    property_name = 'mu'
    functor_names = 'T'
    expression = '4.5e-3'
  []
  [k]
    type = ADParsedFunctorMaterial
    property_name = 'k'
    functor_names = 'T'
    expression = 0.7
  []
[]

[AuxKernels]
  [rho_out]
    type = FunctorAux
    functor = 'rho'
    variable = 'rho_var'
    execute_on = 'NONLINEAR'
  []
  [cp_out]
    type = FunctorAux
    functor = 'cp'
    variable = 'cp_var'
    execute_on = 'NONLINEAR'
  []
  [mu_out]
    type = FunctorAux
    functor = 'mu'
    variable = 'mu_var'
    execute_on = 'NONLINEAR'
  []
  [k_out]
    type = FunctorAux
    functor = 'k'
    variable = 'k_var'
    execute_on = 'NONLINEAR'
  []
  [T_from_h_functor_aux]
    type = FunctorAux
    functor = 'T_from_p_h'
    variable = 'T'
    execute_on = 'NONLINEAR'
  []
  [h_from_T_functor_aux]
    type = FunctorAux
    functor = 'h_from_p_T'
    variable = 'h_aux'
    execute_on = 'NONLINEAR'
  []
[]

[Postprocessors]
  [T_out_sim]
    type = ElementalVariableValue
    variable = T
    elementid = ${fparse nx-1}
  []
  [T_out_analytic]
    type = FunctionValuePostprocessor
    function = T_analytical
  []
[]

[Executioner]
  type = SIMPLE
  momentum_l_abs_tol = 1e-12
  pressure_l_abs_tol = 1e-12
  energy_l_abs_tol = 1e-12
  momentum_l_tol = 0
  pressure_l_tol = 0
  energy_l_tol = 0
  rhie_chow_user_object = 'rc'
  momentum_systems = 'u_system'
  pressure_system = 'pressure_system'
  energy_system = 'energy_system'
  momentum_equation_relaxation = 0.7
  pressure_variable_relaxation = 0.3
  energy_equation_relaxation = 0.95
  num_iterations = 100
  pressure_absolute_tolerance = 1e-8
  momentum_absolute_tolerance = 1e-8
  energy_absolute_tolerance = 1e-6
  print_fields = false
  momentum_l_max_its = 200

  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'
  continue_on_max_its = true
[]

[Outputs]
  [out]
    type = CSV
  []
[]

(moose/modules/navier_stokes/test/tests/finite_volume/wcns/enthalpy_equation/1d_test_h.i)

L = 30
nx = 600
bulk_u = 0.01
q_source = 50000.
A_cp = 976.78
B_cp = 1.0634
T_in = 860.
p_ref = 101325.0
rho = 2000.
advected_interp_method = 'upwind'

[Mesh]
  [gmg]
    type = GeneratedMeshGenerator
    dim = 1
    xmin = 0
    xmax = ${L}
    nx = ${nx}
  []
  allow_renumbering = false
[]

[GlobalParams]
  rhie_chow_user_object = 'rc'
  advected_interp_method = ${advected_interp_method}
  u = vel_x
[]

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

[UserObjects]
  [rc]
    type = RhieChowMassFlux
    u = vel_x
    pressure = pressure
    rho = 'rho'
    p_diffusion_kernel = p_diffusion
  []
[]

[Variables]
  [vel_x]
    type = MooseLinearVariableFVReal
    solver_sys = u_system
    initial_condition = ${bulk_u}
  []
  [pressure]
    type = MooseLinearVariableFVReal
    solver_sys = pressure_system
    initial_condition = ${p_ref}
  []
  [h]
    type = MooseLinearVariableFVReal
    solver_sys = energy_system
    initial_condition = ${fparse 860.*1900.}
  []
[]

[AuxVariables]
  [rho_var]
    type = MooseLinearVariableFVReal
  []
  [cp_var]
    type = MooseLinearVariableFVReal
  []
  [mu_var]
    type = MooseLinearVariableFVReal
  []
  [k_var]
    type = MooseLinearVariableFVReal
  []
  [alpha_var]
    type = MooseLinearVariableFVReal
  []
  [T]
    type = MooseLinearVariableFVReal
    initial_condition = 860.
  []
  [h_aux]
    type = MooseLinearVariableFVReal
  []
[]

[LinearFVKernels]

  [u_advection_stress]
    type = LinearWCNSFVMomentumFlux
    variable = vel_x
    mu = 'mu'
    momentum_component = 'x'
    use_nonorthogonal_correction = false
  []
  [u_pressure]
    type = LinearFVMomentumPressure
    variable = vel_x
    pressure = pressure
    momentum_component = 'x'
  []

  [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
  []

  [temp_advection]
    type = LinearFVEnergyAdvection
    variable = h
  []
  [source]
    type = LinearFVSource
    variable = h
    source_density = source_func
  []
[]

[LinearFVBCs]
  [inlet_u]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'left'
    variable = vel_x
    functor = ${bulk_u} #${bulk_u} #'fully_developed_velocity'
  []
  [inlet_h]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    variable = h
    boundary = 'left'
    functor = 'h_from_p_T'
  []
  [inlet_T]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    variable = T
    boundary = 'left'
    functor = ${T_in}
  []

  [outlet_p]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'right'
    variable = pressure
    functor = ${p_ref}
  []
  [outlet_h]
    type = LinearFVAdvectionDiffusionOutflowBC
    variable = h
    use_two_term_expansion = false
    boundary = 'right'
  []
  [outlet_u]
    type = LinearFVAdvectionDiffusionOutflowBC
    variable = vel_x
    use_two_term_expansion = false
    boundary = 'right'
  []
[]

[Functions]
  [source_func]
    type = ParsedFunction
    expression = ${q_source}
  []
  [T_analytical]
    type = ParsedFunction
    expression = ${fparse (-A_cp+sqrt(A_cp^2-2*B_cp*(-q_source/rho/bulk_u*L-A_cp*T_in-B_cp/2*T_in*T_in)))/B_cp}
  []
[]

[FunctorMaterials]
  [enthalpy_material]
    type = LinearFVEnthalpyFunctorMaterial
    pressure = ${p_ref}
    T_fluid = T
    h = h
    h_from_p_T_functor = h_from_p_T_functor
    T_from_p_h_functor = T_from_p_h_functor
  []
  [h_from_p_T_functor]
    type = ParsedFunctorMaterial
    property_name = 'h_from_p_T_functor'
    functor_names = 'T'
    expression = '${A_cp}*T+${B_cp}/2*(T^2)'
  []
  [T_from_p_h_functor]
    type = ParsedFunctorMaterial
    property_name = 'T_from_p_h_functor'
    functor_names = 'h'
    expression = '(-${A_cp}+sqrt(${A_cp}^2+2*h*${B_cp}))/${B_cp}'
  []
  [rho]
    type = ADParsedFunctorMaterial
    property_name = 'rho'
    functor_names = 'T'
    expression = ${rho}
  []
  [cp]
    type = ADParsedFunctorMaterial
    property_name = 'cp'
    functor_names = 'T'
    expression = '${A_cp}+${B_cp}*T'
  []
  [mu]
    type = ADParsedFunctorMaterial
    property_name = 'mu'
    functor_names = 'T'
    expression = '4.5e-3'
  []
  [k]
    type = ADParsedFunctorMaterial
    property_name = 'k'
    functor_names = 'T'
    expression = 0.7
  []
[]

[AuxKernels]
  [rho_out]
    type = FunctorAux
    functor = 'rho'
    variable = 'rho_var'
    execute_on = 'NONLINEAR'
  []
  [cp_out]
    type = FunctorAux
    functor = 'cp'
    variable = 'cp_var'
    execute_on = 'NONLINEAR'
  []
  [mu_out]
    type = FunctorAux
    functor = 'mu'
    variable = 'mu_var'
    execute_on = 'NONLINEAR'
  []
  [k_out]
    type = FunctorAux
    functor = 'k'
    variable = 'k_var'
    execute_on = 'NONLINEAR'
  []
  [T_from_h_functor_aux]
    type = FunctorAux
    functor = 'T_from_p_h'
    variable = 'T'
    execute_on = 'NONLINEAR'
  []
  [h_from_T_functor_aux]
    type = FunctorAux
    functor = 'h_from_p_T'
    variable = 'h_aux'
    execute_on = 'NONLINEAR'
  []
[]

[Postprocessors]
  [T_out_sim]
    type = ElementalVariableValue
    variable = T
    elementid = ${fparse nx-1}
  []
  [T_out_analytic]
    type = FunctionValuePostprocessor
    function = T_analytical
  []
[]

[Executioner]
  type = SIMPLE
  momentum_l_abs_tol = 1e-12
  pressure_l_abs_tol = 1e-12
  energy_l_abs_tol = 1e-12
  momentum_l_tol = 0
  pressure_l_tol = 0
  energy_l_tol = 0
  rhie_chow_user_object = 'rc'
  momentum_systems = 'u_system'
  pressure_system = 'pressure_system'
  energy_system = 'energy_system'
  momentum_equation_relaxation = 0.7
  pressure_variable_relaxation = 0.3
  energy_equation_relaxation = 0.95
  num_iterations = 100
  pressure_absolute_tolerance = 1e-8
  momentum_absolute_tolerance = 1e-8
  energy_absolute_tolerance = 1e-6
  print_fields = false
  momentum_l_max_its = 200

  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'
  continue_on_max_its = true
[]

[Outputs]
  [out]
    type = CSV
  []
[]

(moose/modules/navier_stokes/test/tests/finite_volume/wcns/enthalpy_equation/1d_test_h.i)

L = 30
nx = 600
bulk_u = 0.01
q_source = 50000.
A_cp = 976.78
B_cp = 1.0634
T_in = 860.
p_ref = 101325.0
rho = 2000.
advected_interp_method = 'upwind'

[Mesh]
  [gmg]
    type = GeneratedMeshGenerator
    dim = 1
    xmin = 0
    xmax = ${L}
    nx = ${nx}
  []
  allow_renumbering = false
[]

[GlobalParams]
  rhie_chow_user_object = 'rc'
  advected_interp_method = ${advected_interp_method}
  u = vel_x
[]

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

[UserObjects]
  [rc]
    type = RhieChowMassFlux
    u = vel_x
    pressure = pressure
    rho = 'rho'
    p_diffusion_kernel = p_diffusion
  []
[]

[Variables]
  [vel_x]
    type = MooseLinearVariableFVReal
    solver_sys = u_system
    initial_condition = ${bulk_u}
  []
  [pressure]
    type = MooseLinearVariableFVReal
    solver_sys = pressure_system
    initial_condition = ${p_ref}
  []
  [h]
    type = MooseLinearVariableFVReal
    solver_sys = energy_system
    initial_condition = ${fparse 860.*1900.}
  []
[]

[AuxVariables]
  [rho_var]
    type = MooseLinearVariableFVReal
  []
  [cp_var]
    type = MooseLinearVariableFVReal
  []
  [mu_var]
    type = MooseLinearVariableFVReal
  []
  [k_var]
    type = MooseLinearVariableFVReal
  []
  [alpha_var]
    type = MooseLinearVariableFVReal
  []
  [T]
    type = MooseLinearVariableFVReal
    initial_condition = 860.
  []
  [h_aux]
    type = MooseLinearVariableFVReal
  []
[]

[LinearFVKernels]

  [u_advection_stress]
    type = LinearWCNSFVMomentumFlux
    variable = vel_x
    mu = 'mu'
    momentum_component = 'x'
    use_nonorthogonal_correction = false
  []
  [u_pressure]
    type = LinearFVMomentumPressure
    variable = vel_x
    pressure = pressure
    momentum_component = 'x'
  []

  [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
  []

  [temp_advection]
    type = LinearFVEnergyAdvection
    variable = h
  []
  [source]
    type = LinearFVSource
    variable = h
    source_density = source_func
  []
[]

[LinearFVBCs]
  [inlet_u]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'left'
    variable = vel_x
    functor = ${bulk_u} #${bulk_u} #'fully_developed_velocity'
  []
  [inlet_h]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    variable = h
    boundary = 'left'
    functor = 'h_from_p_T'
  []
  [inlet_T]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    variable = T
    boundary = 'left'
    functor = ${T_in}
  []

  [outlet_p]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'right'
    variable = pressure
    functor = ${p_ref}
  []
  [outlet_h]
    type = LinearFVAdvectionDiffusionOutflowBC
    variable = h
    use_two_term_expansion = false
    boundary = 'right'
  []
  [outlet_u]
    type = LinearFVAdvectionDiffusionOutflowBC
    variable = vel_x
    use_two_term_expansion = false
    boundary = 'right'
  []
[]

[Functions]
  [source_func]
    type = ParsedFunction
    expression = ${q_source}
  []
  [T_analytical]
    type = ParsedFunction
    expression = ${fparse (-A_cp+sqrt(A_cp^2-2*B_cp*(-q_source/rho/bulk_u*L-A_cp*T_in-B_cp/2*T_in*T_in)))/B_cp}
  []
[]

[FunctorMaterials]
  [enthalpy_material]
    type = LinearFVEnthalpyFunctorMaterial
    pressure = ${p_ref}
    T_fluid = T
    h = h
    h_from_p_T_functor = h_from_p_T_functor
    T_from_p_h_functor = T_from_p_h_functor
  []
  [h_from_p_T_functor]
    type = ParsedFunctorMaterial
    property_name = 'h_from_p_T_functor'
    functor_names = 'T'
    expression = '${A_cp}*T+${B_cp}/2*(T^2)'
  []
  [T_from_p_h_functor]
    type = ParsedFunctorMaterial
    property_name = 'T_from_p_h_functor'
    functor_names = 'h'
    expression = '(-${A_cp}+sqrt(${A_cp}^2+2*h*${B_cp}))/${B_cp}'
  []
  [rho]
    type = ADParsedFunctorMaterial
    property_name = 'rho'
    functor_names = 'T'
    expression = ${rho}
  []
  [cp]
    type = ADParsedFunctorMaterial
    property_name = 'cp'
    functor_names = 'T'
    expression = '${A_cp}+${B_cp}*T'
  []
  [mu]
    type = ADParsedFunctorMaterial
    property_name = 'mu'
    functor_names = 'T'
    expression = '4.5e-3'
  []
  [k]
    type = ADParsedFunctorMaterial
    property_name = 'k'
    functor_names = 'T'
    expression = 0.7
  []
[]

[AuxKernels]
  [rho_out]
    type = FunctorAux
    functor = 'rho'
    variable = 'rho_var'
    execute_on = 'NONLINEAR'
  []
  [cp_out]
    type = FunctorAux
    functor = 'cp'
    variable = 'cp_var'
    execute_on = 'NONLINEAR'
  []
  [mu_out]
    type = FunctorAux
    functor = 'mu'
    variable = 'mu_var'
    execute_on = 'NONLINEAR'
  []
  [k_out]
    type = FunctorAux
    functor = 'k'
    variable = 'k_var'
    execute_on = 'NONLINEAR'
  []
  [T_from_h_functor_aux]
    type = FunctorAux
    functor = 'T_from_p_h'
    variable = 'T'
    execute_on = 'NONLINEAR'
  []
  [h_from_T_functor_aux]
    type = FunctorAux
    functor = 'h_from_p_T'
    variable = 'h_aux'
    execute_on = 'NONLINEAR'
  []
[]

[Postprocessors]
  [T_out_sim]
    type = ElementalVariableValue
    variable = T
    elementid = ${fparse nx-1}
  []
  [T_out_analytic]
    type = FunctionValuePostprocessor
    function = T_analytical
  []
[]

[Executioner]
  type = SIMPLE
  momentum_l_abs_tol = 1e-12
  pressure_l_abs_tol = 1e-12
  energy_l_abs_tol = 1e-12
  momentum_l_tol = 0
  pressure_l_tol = 0
  energy_l_tol = 0
  rhie_chow_user_object = 'rc'
  momentum_systems = 'u_system'
  pressure_system = 'pressure_system'
  energy_system = 'energy_system'
  momentum_equation_relaxation = 0.7
  pressure_variable_relaxation = 0.3
  energy_equation_relaxation = 0.95
  num_iterations = 100
  pressure_absolute_tolerance = 1e-8
  momentum_absolute_tolerance = 1e-8
  energy_absolute_tolerance = 1e-6
  print_fields = false
  momentum_l_max_its = 200

  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'
  continue_on_max_its = true
[]

[Outputs]
  [out]
    type = CSV
  []
[]

(moose/modules/navier_stokes/test/tests/finite_volume/wcns/enthalpy_equation/1d_test_h.i)

L = 30
nx = 600
bulk_u = 0.01
q_source = 50000.
A_cp = 976.78
B_cp = 1.0634
T_in = 860.
p_ref = 101325.0
rho = 2000.
advected_interp_method = 'upwind'

[Mesh]
  [gmg]
    type = GeneratedMeshGenerator
    dim = 1
    xmin = 0
    xmax = ${L}
    nx = ${nx}
  []
  allow_renumbering = false
[]

[GlobalParams]
  rhie_chow_user_object = 'rc'
  advected_interp_method = ${advected_interp_method}
  u = vel_x
[]

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

[UserObjects]
  [rc]
    type = RhieChowMassFlux
    u = vel_x
    pressure = pressure
    rho = 'rho'
    p_diffusion_kernel = p_diffusion
  []
[]

[Variables]
  [vel_x]
    type = MooseLinearVariableFVReal
    solver_sys = u_system
    initial_condition = ${bulk_u}
  []
  [pressure]
    type = MooseLinearVariableFVReal
    solver_sys = pressure_system
    initial_condition = ${p_ref}
  []
  [h]
    type = MooseLinearVariableFVReal
    solver_sys = energy_system
    initial_condition = ${fparse 860.*1900.}
  []
[]

[AuxVariables]
  [rho_var]
    type = MooseLinearVariableFVReal
  []
  [cp_var]
    type = MooseLinearVariableFVReal
  []
  [mu_var]
    type = MooseLinearVariableFVReal
  []
  [k_var]
    type = MooseLinearVariableFVReal
  []
  [alpha_var]
    type = MooseLinearVariableFVReal
  []
  [T]
    type = MooseLinearVariableFVReal
    initial_condition = 860.
  []
  [h_aux]
    type = MooseLinearVariableFVReal
  []
[]

[LinearFVKernels]

  [u_advection_stress]
    type = LinearWCNSFVMomentumFlux
    variable = vel_x
    mu = 'mu'
    momentum_component = 'x'
    use_nonorthogonal_correction = false
  []
  [u_pressure]
    type = LinearFVMomentumPressure
    variable = vel_x
    pressure = pressure
    momentum_component = 'x'
  []

  [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
  []

  [temp_advection]
    type = LinearFVEnergyAdvection
    variable = h
  []
  [source]
    type = LinearFVSource
    variable = h
    source_density = source_func
  []
[]

[LinearFVBCs]
  [inlet_u]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'left'
    variable = vel_x
    functor = ${bulk_u} #${bulk_u} #'fully_developed_velocity'
  []
  [inlet_h]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    variable = h
    boundary = 'left'
    functor = 'h_from_p_T'
  []
  [inlet_T]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    variable = T
    boundary = 'left'
    functor = ${T_in}
  []

  [outlet_p]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'right'
    variable = pressure
    functor = ${p_ref}
  []
  [outlet_h]
    type = LinearFVAdvectionDiffusionOutflowBC
    variable = h
    use_two_term_expansion = false
    boundary = 'right'
  []
  [outlet_u]
    type = LinearFVAdvectionDiffusionOutflowBC
    variable = vel_x
    use_two_term_expansion = false
    boundary = 'right'
  []
[]

[Functions]
  [source_func]
    type = ParsedFunction
    expression = ${q_source}
  []
  [T_analytical]
    type = ParsedFunction
    expression = ${fparse (-A_cp+sqrt(A_cp^2-2*B_cp*(-q_source/rho/bulk_u*L-A_cp*T_in-B_cp/2*T_in*T_in)))/B_cp}
  []
[]

[FunctorMaterials]
  [enthalpy_material]
    type = LinearFVEnthalpyFunctorMaterial
    pressure = ${p_ref}
    T_fluid = T
    h = h
    h_from_p_T_functor = h_from_p_T_functor
    T_from_p_h_functor = T_from_p_h_functor
  []
  [h_from_p_T_functor]
    type = ParsedFunctorMaterial
    property_name = 'h_from_p_T_functor'
    functor_names = 'T'
    expression = '${A_cp}*T+${B_cp}/2*(T^2)'
  []
  [T_from_p_h_functor]
    type = ParsedFunctorMaterial
    property_name = 'T_from_p_h_functor'
    functor_names = 'h'
    expression = '(-${A_cp}+sqrt(${A_cp}^2+2*h*${B_cp}))/${B_cp}'
  []
  [rho]
    type = ADParsedFunctorMaterial
    property_name = 'rho'
    functor_names = 'T'
    expression = ${rho}
  []
  [cp]
    type = ADParsedFunctorMaterial
    property_name = 'cp'
    functor_names = 'T'
    expression = '${A_cp}+${B_cp}*T'
  []
  [mu]
    type = ADParsedFunctorMaterial
    property_name = 'mu'
    functor_names = 'T'
    expression = '4.5e-3'
  []
  [k]
    type = ADParsedFunctorMaterial
    property_name = 'k'
    functor_names = 'T'
    expression = 0.7
  []
[]

[AuxKernels]
  [rho_out]
    type = FunctorAux
    functor = 'rho'
    variable = 'rho_var'
    execute_on = 'NONLINEAR'
  []
  [cp_out]
    type = FunctorAux
    functor = 'cp'
    variable = 'cp_var'
    execute_on = 'NONLINEAR'
  []
  [mu_out]
    type = FunctorAux
    functor = 'mu'
    variable = 'mu_var'
    execute_on = 'NONLINEAR'
  []
  [k_out]
    type = FunctorAux
    functor = 'k'
    variable = 'k_var'
    execute_on = 'NONLINEAR'
  []
  [T_from_h_functor_aux]
    type = FunctorAux
    functor = 'T_from_p_h'
    variable = 'T'
    execute_on = 'NONLINEAR'
  []
  [h_from_T_functor_aux]
    type = FunctorAux
    functor = 'h_from_p_T'
    variable = 'h_aux'
    execute_on = 'NONLINEAR'
  []
[]

[Postprocessors]
  [T_out_sim]
    type = ElementalVariableValue
    variable = T
    elementid = ${fparse nx-1}
  []
  [T_out_analytic]
    type = FunctionValuePostprocessor
    function = T_analytical
  []
[]

[Executioner]
  type = SIMPLE
  momentum_l_abs_tol = 1e-12
  pressure_l_abs_tol = 1e-12
  energy_l_abs_tol = 1e-12
  momentum_l_tol = 0
  pressure_l_tol = 0
  energy_l_tol = 0
  rhie_chow_user_object = 'rc'
  momentum_systems = 'u_system'
  pressure_system = 'pressure_system'
  energy_system = 'energy_system'
  momentum_equation_relaxation = 0.7
  pressure_variable_relaxation = 0.3
  energy_equation_relaxation = 0.95
  num_iterations = 100
  pressure_absolute_tolerance = 1e-8
  momentum_absolute_tolerance = 1e-8
  energy_absolute_tolerance = 1e-6
  print_fields = false
  momentum_l_max_its = 200

  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'
  continue_on_max_its = true
[]

[Outputs]
  [out]
    type = CSV
  []
[]

Example input syntax 1 : Fluid Properties
Example input syntax 2 : User - Defined Properties
Input Parameters

Usage

Development

Demonstration

LinearFVEnthalpyFunctorMaterial

Example input syntax 1: Fluid Properties

Example input syntax 2: User-Defined Properties

Input Parameters

Required Parameters

Optional Parameters

Advanced Parameters

Outputs Parameters