INSADHeatConductionTimeDerivative

Description

The INSADHeatConductionTimeDerivative kernel implements a time derivative for the domain $var element = document.getElementById("moose-equation-fc96a66c-a2ae-412f-8cc2-60e23b500ac6");katex.render("\\Omega", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ given by

$var element = document.getElementById("moose-equation-08720402-97d6-4a82-89ff-0e258b196bc1");katex.render("\\underbrace{\\rho c_p \\frac{\\partial u}{\\partial t}}_{\\textrm{INSADHeatConductionTimeDerivative}} + \\sum_{i=1}^n \\beta_i = 0 \\in \\Omega.", element, {displayMode:true,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ where $var element = document.getElementById("moose-equation-da3ee310-2207-4ef2-a9af-f33d049a45b2");katex.render("\\rho", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ is the material density, $var element = document.getElementById("moose-equation-4d50e343-5895-4c74-af08-a7287a69e0d1");katex.render("c_p", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ is the specific heat, and the second term on the left hand side corresponds to the strong forms of other kernels. The corresponding INSADHeatConductionTimeDerivative weak form using inner-product notation is

$var element = document.getElementById("moose-equation-98cae184-8125-4a45-adb0-12e2b3e6ecee");katex.render("R_i(u_h) = (\\psi_i, \\rho c_p\\frac{\\partial u_h}{\\partial t}) \\quad \\forall \\psi_i,", element, {displayMode:true,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ where $var element = document.getElementById("moose-equation-870cedda-5fed-4f75-9b78-c450a324736e");katex.render("u_h", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ is the approximate solution and $var element = document.getElementById("moose-equation-ffcdfbe5-d6b7-4823-be6e-8dd4a680fa2e");katex.render("\\psi_i", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ is a finite element test function.

The Jacobian is given by automatic differentiation, and should be perfect as long as $var element = document.getElementById("moose-equation-3e7a5911-dfed-4e81-b7c9-246f2b641104");katex.render("c_p", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ and $var element = document.getElementById("moose-equation-ebb71def-15ec-4ca0-a370-97d57ee0af7e");katex.render("\\rho", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ are provided using ADMaterial derived objects.

Input Parameters

variableThe name of the variable that this residual object operates on
C++ Type:NonlinearVariableName
Options:
Description:The name of the variable that this residual object operates on

Required Parameters

blockThe list of block ids (SubdomainID) that this object will be applied
C++ Type:std::vector<SubdomainName>
Options:
Description:The list of block ids (SubdomainID) that this object will be applied
displacementsThe displacements
C++ Type:std::vector<VariableName>
Options:
Description:The displacements

Optional Parameters

control_tagsAdds user-defined labels for accessing object parameters via control logic.
C++ Type:std::vector<std::string>
Options:
Description:Adds user-defined labels for accessing object parameters via control logic.
diag_save_inThe name of auxiliary variables to save this Kernel's diagonal Jacobian contributions to. Everything about that variable must match everything about this variable (the type, what blocks it's on, etc.)
C++ Type:std::vector<AuxVariableName>
Options:
Description:The name of auxiliary variables to save this Kernel's diagonal Jacobian contributions to. Everything about that variable must match everything about this variable (the type, what blocks it's on, etc.)
enableTrueSet the enabled status of the MooseObject.
Default:True
C++ Type:bool
Options:
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
Options:
Description:Determines whether this object is calculated using an implicit or explicit form
save_inThe name of auxiliary variables to save this Kernel's residual contributions to. Everything about that variable must match everything about this variable (the type, what blocks it's on, etc.)
C++ Type:std::vector<AuxVariableName>
Options:
Description:The name of auxiliary variables to save this Kernel's residual contributions to. Everything about that variable must match everything about this variable (the type, what blocks it's on, etc.)
seed0The seed for the master random number generator
Default:0
C++ Type:unsigned int
Options:
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
Options:
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

extra_matrix_tagsThe extra tags for the matrices this Kernel should fill
C++ Type:std::vector<TagName>
Options:
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>
Options:
Description:The extra tags for the vectors this Kernel should fill
matrix_tagssystem timeThe tag for the matrices this Kernel should fill
Default:system time
C++ Type:MultiMooseEnum
Options:nontime, system, time
Description:The tag for the matrices this Kernel should fill
vector_tagstimeThe tag for the vectors this Kernel should fill
Default:time
C++ Type:MultiMooseEnum
Options:nontime, time
Description:The tag for the vectors this Kernel should fill

Tagging Parameters

Input Files

(modules/navier_stokes/test/tests/ins/block-restriction/two-mats-two-eqn-sets.i)
(modules/navier_stokes/test/tests/ins/block-restriction/one-mat-two-eqn-sets.i)
(modules/navier_stokes/test/tests/ins/lid_driven/ad_lid_driven.i)
(modules/navier_stokes/test/tests/ins/block-restriction/two-mats-one-eqn-set.i)
(modules/navier_stokes/test/tests/ins/lid_driven/ad_lid_driven_mean_zero_pressure.i)
(modules/navier_stokes/test/tests/ins/lid_driven/ad_lid_driven_stabilized_with_temp_transient.i)

(modules/navier_stokes/test/tests/ins/block-restriction/two-mats-two-eqn-sets.i)

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 2
    xmin = 0
    xmax = 2
    ymin = 0
    ymax = 1
    nx = 16
    ny = 8
    elem_type = QUAD9
  []
  [./corner_node_0]
    type = ExtraNodesetGenerator
    new_boundary = 'pinned_node_0'
    coord = '0 0 0'
    input = gen
  [../]
  [./corner_node_1]
    type = ExtraNodesetGenerator
    new_boundary = 'pinned_node_1'
    coord = '1 0 0'
    input = corner_node_0
  [../]
  [./subdomain1]
    input = corner_node_1
    type = SubdomainBoundingBoxGenerator
    bottom_left = '1 0 0'
    top_right = '2 1 0'
    block_id = 1
  [../]
  [./break_boundary]
    input = subdomain1
    type = BreakBoundaryOnSubdomainGenerator
  [../]
  [./interface0]
    type = SideSetsBetweenSubdomainsGenerator
    input = break_boundary
    primary_block = '0'
    paired_block = '1'
    new_boundary = 'interface0'
  [../]
  [./interface1]
    type = SideSetsBetweenSubdomainsGenerator
    input = interface0
    primary_block = '1'
    paired_block = '0'
    new_boundary = 'interface1'
  [../]
[]

[Variables]
  [velocity0]
    order = SECOND
    family = LAGRANGE_VEC
    block = 0
  []
  [T0]
    order = SECOND
    [InitialCondition]
      type = ConstantIC
      value = 1.0
    []
    block = 0
  []
  [p0]
    block = 0
  []

  [velocity1]
    order = SECOND
    family = LAGRANGE_VEC
    block = 1
  []
  [T1]
    order = SECOND
    [InitialCondition]
      type = ConstantIC
      value = 1.0
    []
    block = 1
  []
  [p1]
    block = 1
  []
[]

[Kernels]
  [./mass0]
    type = INSADMass
    variable = p0
    block = 0
  [../]
  [./momentum_time0]
    type = INSADMomentumTimeDerivative
    variable = velocity0
    block = 0
  [../]
  [./momentum_convection0]
    type = INSADMomentumAdvection
    variable = velocity0
    block = 0
  [../]
  [./momentum_viscous0]
    type = INSADMomentumViscous
    variable = velocity0
    block = 0
  [../]
  [./momentum_pressure0]
    type = INSADMomentumPressure
    variable = velocity0
    p = p0
    integrate_p_by_parts = true
    block = 0
  [../]
  [./temperature_time0]
    type = INSADHeatConductionTimeDerivative
    variable = T0
    block = 0
  [../]
  [./temperature_advection0]
    type = INSADEnergyAdvection
    variable = T0
    block = 0
  [../]
  [./temperature_conduction0]
    type = ADHeatConduction
    variable = T0
    thermal_conductivity = 'k'
    block = 0
  [../]

  [./mass1]
    type = INSADMass
    variable = p1
    block = 1
  [../]
  [./momentum_time1]
    type = INSADMomentumTimeDerivative
    variable = velocity1
    block = 1
  [../]
  [./momentum_convection1]
    type = INSADMomentumAdvection
    variable = velocity1
    block = 1
  [../]
  [./momentum_viscous1]
    type = INSADMomentumViscous
    variable = velocity1
    block = 1
  [../]
  [./momentum_pressure1]
    type = INSADMomentumPressure
    variable = velocity1
    p = p1
    integrate_p_by_parts = true
    block = 1
  [../]
  [./temperature_time1]
    type = INSADHeatConductionTimeDerivative
    variable = T1
    block = 1
  [../]
  [./temperature_advection1]
    type = INSADEnergyAdvection
    variable = T1
    block = 1
  [../]
  [./temperature_conduction1]
    type = ADHeatConduction
    variable = T1
    thermal_conductivity = 'k'
    block = 1
  [../]
[]

[BCs]
  [./no_slip0]
    type = VectorFunctionDirichletBC
    variable = velocity0
    boundary = 'bottom_to_0 interface0 left'
  [../]
  [./lid0]
    type = VectorFunctionDirichletBC
    variable = velocity0
    boundary = 'top_to_0'
    function_x = 'lid_function0'
  [../]
  [./T_hot0]
    type = DirichletBC
    variable = T0
    boundary = 'bottom_to_0'
    value = 1
  [../]
  [./T_cold0]
    type = DirichletBC
    variable = T0
    boundary = 'top_to_0'
    value = 0
  [../]
  [./pressure_pin0]
    type = DirichletBC
    variable = p0
    boundary = 'pinned_node_0'
    value = 0
  [../]

  [./no_slip1]
    type = VectorFunctionDirichletBC
    variable = velocity1
    boundary = 'bottom_to_1 interface1 right'
  [../]
  [./lid1]
    type = VectorFunctionDirichletBC
    variable = velocity1
    boundary = 'top_to_1'
    function_x = 'lid_function1'
  [../]
  [./T_hot1]
    type = DirichletBC
    variable = T1
    boundary = 'bottom_to_1'
    value = 1
  [../]
  [./T_cold1]
    type = DirichletBC
    variable = T1
    boundary = 'top_to_1'
    value = 0
  [../]
  [./pressure_pin1]
    type = DirichletBC
    variable = p1
    boundary = 'pinned_node_1'
    value = 0
  [../]
[]

[Materials]
  [./const]
    type = ADGenericConstantMaterial
    prop_names = 'rho mu cp k'
    prop_values = '1  1  1  .01'
  [../]
  [ins_mat0]
    type = INSAD3Eqn
    velocity = velocity0
    pressure = p0
    temperature = T0
    block = 0
  []
  [ins_mat1]
    type = INSAD3Eqn
    velocity = velocity1
    pressure = p1
    temperature = T1
    block = 1
  []
[]

[Functions]
    # We pick a function that is exactly represented in the velocity
    # space so that the Dirichlet conditions are the same regardless
    # of the mesh spacing.
  [./lid_function0]
    type = ParsedFunction
    value = '4*x*(1-x)'
  [../]
  [./lid_function1]
    type = ParsedFunction
    value = '4*(x-1)*(2-x)'
  [../]
[]

[Preconditioning]
  [./SMP]
    type = SMP
    full = true
    solve_type = 'NEWTON'
  [../]
[]

[Executioner]
  type = Transient
  # Run for 100+ timesteps to reach steady state.
  num_steps = 5
  dt = .5
  dtmin = .5
  petsc_options_iname = '-pc_type -pc_asm_overlap -sub_pc_type -sub_pc_factor_levels -sub_pc_factor_shift_type'
  petsc_options_value = 'asm      2               ilu          4                     NONZERO'
  line_search = 'none'
  nl_rel_tol = 1e-12
  nl_abs_tol = 1e-13
  nl_max_its = 6
  l_tol = 1e-6
  l_max_its = 500
[]

[Outputs]
  exodus = true
[]

(modules/navier_stokes/test/tests/ins/block-restriction/one-mat-two-eqn-sets.i)

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 2
    xmin = 0
    xmax = 2
    ymin = 0
    ymax = 1
    nx = 16
    ny = 8
    elem_type = QUAD9
  []
  [./corner_node_0]
    type = ExtraNodesetGenerator
    new_boundary = 'pinned_node_0'
    coord = '0 0 0'
    input = gen
  [../]
  [./corner_node_1]
    type = ExtraNodesetGenerator
    new_boundary = 'pinned_node_1'
    coord = '1 0 0'
    input = corner_node_0
  [../]
  [./subdomain1]
    input = corner_node_1
    type = SubdomainBoundingBoxGenerator
    bottom_left = '1 0 0'
    top_right = '2 1 0'
    block_id = 1
  [../]
  [./break_boundary]
    input = subdomain1
    type = BreakBoundaryOnSubdomainGenerator
  [../]
  [./interface0]
    type = SideSetsBetweenSubdomainsGenerator
    input = break_boundary
    primary_block = '0'
    paired_block = '1'
    new_boundary = 'interface0'
  [../]
  [./interface1]
    type = SideSetsBetweenSubdomainsGenerator
    input = interface0
    primary_block = '1'
    paired_block = '0'
    new_boundary = 'interface1'
  [../]
[]

[Variables]
  [velocity0]
    order = SECOND
    family = LAGRANGE_VEC
  []
  [T0]
    order = SECOND
    [InitialCondition]
      type = ConstantIC
      value = 1.0
    []
  []
  [p0]
  []
[]

[Kernels]
  [./mass0]
    type = INSADMass
    variable = p0
    block = 0
  [../]
  [./momentum_time0]
    type = INSADMomentumTimeDerivative
    variable = velocity0
    block = 0
  [../]
  [./momentum_convection0]
    type = INSADMomentumAdvection
    variable = velocity0
    block = 0
  [../]
  [./momentum_viscous0]
    type = INSADMomentumViscous
    variable = velocity0
    block = 0
  [../]
  [./momentum_pressure0]
    type = INSADMomentumPressure
    variable = velocity0
    p = p0
    integrate_p_by_parts = true
    block = 0
  [../]
  [./temperature_time0]
    type = INSADHeatConductionTimeDerivative
    variable = T0
    block = 0
  [../]
  [./temperature_advection0]
    type = INSADEnergyAdvection
    variable = T0
    block = 0
  [../]
  [./temperature_conduction0]
    type = ADHeatConduction
    variable = T0
    thermal_conductivity = 'k'
    block = 0
  [../]

  [./mass1]
    type = INSADMass
    variable = p0
    block = 1
  [../]
  [./momentum_time1]
    type = INSADMomentumTimeDerivative
    variable = velocity0
    block = 1
  [../]
  [./momentum_convection1]
    type = INSADMomentumAdvection
    variable = velocity0
    block = 1
  [../]
  [./momentum_viscous1]
    type = INSADMomentumViscous
    variable = velocity0
    block = 1
  [../]
  [./momentum_pressure1]
    type = INSADMomentumPressure
    variable = velocity0
    p = p0
    integrate_p_by_parts = true
    block = 1
  [../]
  [./temperature_time1]
    type = INSADHeatConductionTimeDerivative
    variable = T0
    block = 1
  [../]
  [./temperature_advection1]
    type = INSADEnergyAdvection
    variable = T0
    block = 1
  [../]
  [./temperature_conduction1]
    type = ADHeatConduction
    variable = T0
    thermal_conductivity = 'k'
    block = 1
  [../]
[]

[BCs]
  [./no_slip0]
    type = VectorFunctionDirichletBC
    variable = velocity0
    boundary = 'bottom_to_0 interface0 left'
  [../]
  [./lid0]
    type = VectorFunctionDirichletBC
    variable = velocity0
    boundary = 'top_to_0'
    function_x = 'lid_function0'
  [../]
  [./T_hot0]
    type = DirichletBC
    variable = T0
    boundary = 'bottom_to_0'
    value = 1
  [../]
  [./T_cold0]
    type = DirichletBC
    variable = T0
    boundary = 'top_to_0'
    value = 0
  [../]
  [./pressure_pin0]
    type = DirichletBC
    variable = p0
    boundary = 'pinned_node_0'
    value = 0
  [../]

  [./no_slip1]
    type = VectorFunctionDirichletBC
    variable = velocity0
    boundary = 'bottom_to_1 interface1 right'
  [../]
  [./lid1]
    type = VectorFunctionDirichletBC
    variable = velocity0
    boundary = 'top_to_1'
    function_x = 'lid_function1'
  [../]
  [./T_hot1]
    type = DirichletBC
    variable = T0
    boundary = 'bottom_to_1'
    value = 1
  [../]
  [./T_cold1]
    type = DirichletBC
    variable = T0
    boundary = 'top_to_1'
    value = 0
  [../]
[]

[Materials]
  [./const]
    type = ADGenericConstantMaterial
    prop_names = 'rho mu cp k'
    prop_values = '1  1  1  .01'
  [../]
  [ins_mat0]
    type = INSAD3Eqn
    velocity = velocity0
    pressure = p0
    temperature = T0
    block = '0 1'
  []
[]

[Functions]
    # We pick a function that is exactly represented in the velocity
    # space so that the Dirichlet conditions are the same regardless
    # of the mesh spacing.
  [./lid_function0]
    type = ParsedFunction
    value = '4*x*(1-x)'
  [../]
  [./lid_function1]
    type = ParsedFunction
    value = '4*(x-1)*(2-x)'
  [../]
[]

[Preconditioning]
  [./SMP]
    type = SMP
    full = true
    solve_type = 'NEWTON'
  [../]
[]

[Executioner]
  type = Transient
  # Run for 100+ timesteps to reach steady state.
  num_steps = 5
  dt = .5
  dtmin = .5
  petsc_options_iname = '-pc_type -pc_asm_overlap -sub_pc_type -sub_pc_factor_levels -sub_pc_factor_shift_type'
  petsc_options_value = 'asm      2               ilu          4                     NONZERO'
  line_search = 'none'
  nl_rel_tol = 1e-12
  nl_abs_tol = 1e-13
  nl_max_its = 6
  l_tol = 1e-6
  l_max_its = 500
[]

[Outputs]
  exodus = true
[]

(modules/navier_stokes/test/tests/ins/lid_driven/ad_lid_driven.i)

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 2
    xmin = 0
    xmax = 1.0
    ymin = 0
    ymax = 1.0
    nx = 16
    ny = 16
    elem_type = QUAD9
  []
  [./corner_node]
    type = ExtraNodesetGenerator
    new_boundary = 'pinned_node'
    nodes = '0'
    input = gen
  [../]
[]

[AuxVariables]
  [vel_x]
    order = SECOND
  []
  [vel_y]
    order = SECOND
  []
[]

[AuxKernels]
  [vel_x]
    type = VectorVariableComponentAux
    variable = vel_x
    vector_variable = velocity
    component = 'x'
  []
  [vel_y]
    type = VectorVariableComponentAux
    variable = vel_y
    vector_variable = velocity
    component = 'y'
  []
[]

[Variables]
  [./velocity]
    order = SECOND
    family = LAGRANGE_VEC
  [../]

  [./T]
    order = SECOND
    [./InitialCondition]
      type = ConstantIC
      value = 1.0
    [../]
  [../]

  [./p]
  [../]
[]

[Kernels]
  [./mass]
    type = INSADMass
    variable = p
  [../]

  [./momentum_time]
    type = INSADMomentumTimeDerivative
    variable = velocity
  [../]

  [./momentum_convection]
    type = INSADMomentumAdvection
    variable = velocity
  [../]

  [./momentum_viscous]
    type = INSADMomentumViscous
    variable = velocity
  [../]

  [./momentum_pressure]
    type = INSADMomentumPressure
    variable = velocity
    p = p
    integrate_p_by_parts = true
  [../]

 [./temperature_time]
   type = INSADHeatConductionTimeDerivative
   variable = T
 [../]

 [./temperature_advection]
   type = INSADEnergyAdvection
   variable = T
 [../]

 [./temperature_conduction]
   type = ADHeatConduction
   variable = T
   thermal_conductivity = 'k'
 [../]
[]

[BCs]
  [./no_slip]
    type = VectorFunctionDirichletBC
    variable = velocity
    boundary = 'bottom right left'
  [../]

  [./lid]
    type = VectorFunctionDirichletBC
    variable = velocity
    boundary = 'top'
    function_x = 'lid_function'
  [../]

  [./T_hot]
    type = DirichletBC
    variable = T
    boundary = 'bottom'
    value = 1
  [../]

  [./T_cold]
    type = DirichletBC
    variable = T
    boundary = 'top'
    value = 0
  [../]

  [./pressure_pin]
    type = DirichletBC
    variable = p
    boundary = 'pinned_node'
    value = 0
  [../]
[]

[Materials]
  [./const]
    type = ADGenericConstantMaterial
    prop_names = 'rho mu cp k'
    prop_values = '1  1  1  .01'
  [../]
  [ins_mat]
    type = INSAD3Eqn
    velocity = velocity
    pressure = p
    temperature = T
  []
[]

[Functions]
  [./lid_function]
    # We pick a function that is exactly represented in the velocity
    # space so that the Dirichlet conditions are the same regardless
    # of the mesh spacing.
    type = ParsedFunction
    value = '4*x*(1-x)'
  [../]
[]

[Preconditioning]
  [./SMP]
    type = SMP
    full = true
    solve_type = 'NEWTON'
  [../]
[]

[Executioner]
  type = Transient
  # Run for 100+ timesteps to reach steady state.
  num_steps = 5
  dt = .5
  dtmin = .5
  petsc_options_iname = '-pc_type -pc_asm_overlap -sub_pc_type -sub_pc_factor_levels'
  petsc_options_value = 'asm      2               ilu          4'
  line_search = 'none'
  nl_rel_tol = 1e-12
  nl_abs_tol = 1e-13
  nl_max_its = 6
  l_tol = 1e-6
  l_max_its = 500
[]

[Outputs]
  file_base = lid_driven_out
  exodus = true
  perf_graph = true
[]

(modules/navier_stokes/test/tests/ins/block-restriction/two-mats-one-eqn-set.i)

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 2
    xmin = 0
    xmax = 2
    ymin = 0
    ymax = 1
    nx = 16
    ny = 8
    elem_type = QUAD9
  []
  [./corner_node_0]
    type = ExtraNodesetGenerator
    new_boundary = 'pinned_node_0'
    coord = '0 0 0'
    input = gen
  [../]
  [./corner_node_1]
    type = ExtraNodesetGenerator
    new_boundary = 'pinned_node_1'
    coord = '1 0 0'
    input = corner_node_0
  [../]
  [./subdomain1]
    input = corner_node_1
    type = SubdomainBoundingBoxGenerator
    bottom_left = '1 0 0'
    top_right = '2 1 0'
    block_id = 1
  [../]
  [./break_boundary]
    input = subdomain1
    type = BreakBoundaryOnSubdomainGenerator
  [../]
  [./interface0]
    type = SideSetsBetweenSubdomainsGenerator
    input = break_boundary
    primary_block = '0'
    paired_block = '1'
    new_boundary = 'interface0'
  [../]
  [./interface1]
    type = SideSetsBetweenSubdomainsGenerator
    input = interface0
    primary_block = '1'
    paired_block = '0'
    new_boundary = 'interface1'
  [../]
[]

[Variables]
  [velocity0]
    order = SECOND
    family = LAGRANGE_VEC
  []
  [T0]
    order = SECOND
    [InitialCondition]
      type = ConstantIC
      value = 1.0
    []
  []
  [p0]
  []
[]

[Kernels]
  [./mass0]
    type = INSADMass
    variable = p0
  [../]
  [./momentum_time0]
    type = INSADMomentumTimeDerivative
    variable = velocity0
  [../]
  [./momentum_convection0]
    type = INSADMomentumAdvection
    variable = velocity0
  [../]
  [./momentum_viscous0]
    type = INSADMomentumViscous
    variable = velocity0
  [../]
  [./momentum_pressure0]
    type = INSADMomentumPressure
    variable = velocity0
    p = p0
    integrate_p_by_parts = true
  [../]
  [./temperature_time0]
    type = INSADHeatConductionTimeDerivative
    variable = T0
  [../]
  [./temperature_advection0]
    type = INSADEnergyAdvection
    variable = T0
  [../]
  [./temperature_conduction0]
    type = ADHeatConduction
    variable = T0
    thermal_conductivity = 'k'
  [../]
[]

[BCs]
  [./no_slip0]
    type = VectorFunctionDirichletBC
    variable = velocity0
    boundary = 'bottom_to_0 interface0 left'
  [../]
  [./lid0]
    type = VectorFunctionDirichletBC
    variable = velocity0
    boundary = 'top_to_0'
    function_x = 'lid_function0'
  [../]
  [./T_hot0]
    type = DirichletBC
    variable = T0
    boundary = 'bottom_to_0'
    value = 1
  [../]
  [./T_cold0]
    type = DirichletBC
    variable = T0
    boundary = 'top_to_0'
    value = 0
  [../]
  [./pressure_pin0]
    type = DirichletBC
    variable = p0
    boundary = 'pinned_node_0'
    value = 0
  [../]

  [./no_slip1]
    type = VectorFunctionDirichletBC
    variable = velocity0
    boundary = 'bottom_to_1 interface1 right'
  [../]
  [./lid1]
    type = VectorFunctionDirichletBC
    variable = velocity0
    boundary = 'top_to_1'
    function_x = 'lid_function1'
  [../]
  [./T_hot1]
    type = DirichletBC
    variable = T0
    boundary = 'bottom_to_1'
    value = 1
  [../]
  [./T_cold1]
    type = DirichletBC
    variable = T0
    boundary = 'top_to_1'
    value = 0
  [../]
[]

[Materials]
  [./const]
    type = ADGenericConstantMaterial
    prop_names = 'rho mu cp k'
    prop_values = '1  1  1  .01'
  [../]
  [ins_mat0]
    type = INSAD3Eqn
    velocity = velocity0
    pressure = p0
    temperature = T0
    block = '0'
  []
  [ins_mat1]
    type = INSAD3Eqn
    velocity = velocity0
    pressure = p0
    temperature = T0
    block = '1'
  []
[]

[Functions]
    # We pick a function that is exactly represented in the velocity
    # space so that the Dirichlet conditions are the same regardless
    # of the mesh spacing.
  [./lid_function0]
    type = ParsedFunction
    value = '4*x*(1-x)'
  [../]
  [./lid_function1]
    type = ParsedFunction
    value = '4*(x-1)*(2-x)'
  [../]
[]

[Preconditioning]
  [./SMP]
    type = SMP
    full = true
    solve_type = 'NEWTON'
  [../]
[]

[Executioner]
  type = Transient
  # Run for 100+ timesteps to reach steady state.
  num_steps = 5
  dt = .5
  dtmin = .5
  petsc_options_iname = '-pc_type -pc_asm_overlap -sub_pc_type -sub_pc_factor_levels -sub_pc_factor_shift_type'
  petsc_options_value = 'asm      2               ilu          4                     NONZERO'
  line_search = 'none'
  nl_rel_tol = 1e-12
  nl_abs_tol = 1e-13
  nl_max_its = 6
  l_tol = 1e-6
  l_max_its = 500
[]

[Outputs]
  exodus = true
[]

(modules/navier_stokes/test/tests/ins/lid_driven/ad_lid_driven_mean_zero_pressure.i)

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 2
    xmin = 0
    xmax = 1.0
    ymin = 0
    ymax = 1.0
    nx = 16
    ny = 16
    elem_type = QUAD9
  []
[]

[AuxVariables]
  [vel_x]
    order = SECOND
  []
  [vel_y]
    order = SECOND
  []
[]

[AuxKernels]
  [vel_x]
    type = VectorVariableComponentAux
    variable = vel_x
    vector_variable = velocity
    component = 'x'
  []
  [vel_y]
    type = VectorVariableComponentAux
    variable = vel_y
    vector_variable = velocity
    component = 'y'
  []
[]

[Variables]
  [./velocity]
    order = SECOND
    family = LAGRANGE_VEC
  [../]

  [./T]
    order = SECOND
    [./InitialCondition]
      type = ConstantIC
      value = 1.0
    [../]
  [../]

  [./p]
  [../]

  [./lambda]
    family = SCALAR
    order = FIRST
  [../]
[]

[Kernels]
  [./mass]
    type = INSADMass
    variable = p
  [../]

  [./momentum_time]
    type = INSADMomentumTimeDerivative
    variable = velocity
  [../]

  [./momentum_convection]
    type = INSADMomentumAdvection
    variable = velocity
  [../]

  [./momentum_viscous]
    type = INSADMomentumViscous
    variable = velocity
  [../]

  [./momentum_pressure]
    type = INSADMomentumPressure
    variable = velocity
    p = p
    integrate_p_by_parts = true
  [../]

 [./temperature_time]
   type = INSADHeatConductionTimeDerivative
   variable = T
 [../]

 [./temperature_advection]
   type = INSADEnergyAdvection
   variable = T
 [../]

 [./temperature_conduction]
   type = ADHeatConduction
   variable = T
   thermal_conductivity = 'k'
 [../]

 [./mean_zero_pressure]
    type = ScalarLagrangeMultiplier
    variable = p
    lambda = lambda
  [../]
[]

[ScalarKernels]
  [./mean_zero_pressure_lm]
    type = AverageValueConstraint
    variable = lambda
    pp_name = pressure_integral
    value = 0
  [../]
[]

[BCs]
  [./no_slip]
    type = VectorFunctionDirichletBC
    variable = velocity
    boundary = 'bottom right left'
  [../]

  [./lid]
    type = VectorFunctionDirichletBC
    variable = velocity
    boundary = 'top'
    function_x = 'lid_function'
  [../]

  [./T_hot]
    type = DirichletBC
    variable = T
    boundary = 'bottom'
    value = 1
  [../]

  [./T_cold]
    type = DirichletBC
    variable = T
    boundary = 'top'
    value = 0
  [../]
[]

[Materials]
  [./const]
    type = ADGenericConstantMaterial
    prop_names = 'rho mu cp k'
    prop_values = '1  1  1  .01'
  [../]
  [ins_mat]
    type = INSAD3Eqn
    velocity = velocity
    pressure = p
    temperature = T
  []
[]

[Postprocessors]
  [./pressure_integral]
    type = ElementIntegralVariablePostprocessor
    variable = p
    execute_on = linear
  [../]
[]

[Functions]
  [./lid_function]
    # We pick a function that is exactly represented in the velocity
    # space so that the Dirichlet conditions are the same regardless
    # of the mesh spacing.
    type = ParsedFunction
    value = '4*x*(1-x)'
  [../]
[]

[Preconditioning]
  [./SMP]
    type = SMP
    full = true
    solve_type = 'NEWTON'
  [../]
[]

[Executioner]
  type = Transient
  # Run for 100+ timesteps to reach steady state.
  num_steps = 5
  dt = .5
  dtmin = .5
  petsc_options_iname = '-pc_type -pc_asm_overlap -sub_pc_type -sub_pc_factor_levels -sub_pc_factor_shift_type'
  petsc_options_value = 'asm      2               ilu          4                     NONZERO'
  line_search = 'none'
  nl_rel_tol = 1e-12
  nl_abs_tol = 1e-13
  nl_max_its = 6
  l_tol = 1e-6
  l_max_its = 500
[]

[Outputs]
  exodus = true
  perf_graph = true
[]

(modules/navier_stokes/test/tests/ins/lid_driven/ad_lid_driven_stabilized_with_temp_transient.i)

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 2
    xmin = 0
    xmax = 1.0
    ymin = 0
    ymax = 1.0
    nx = 16
    ny = 16
  []
  [./corner_node]
    type = ExtraNodesetGenerator
    new_boundary = 'pinned_node'
    nodes = '0'
    input = gen
  [../]
[]

[Variables]
  [./velocity]
    family = LAGRANGE_VEC
  [../]
  [./p]
  [../]
  [temperature]
    [InitialCondition]
      type = ConstantIC
      value = 1.0
    []
  []
[]

[ICs]
  [velocity]
    type = VectorConstantIC
    x_value = 1e-15
    y_value = 1e-15
    variable = velocity
  []
[]

[Kernels]
  [./mass]
    type = INSADMass
    variable = p
  [../]
  [./mass_pspg]
    type = INSADMassPSPG
    variable = p
  [../]

  [./momentum_time]
    type = INSADMomentumTimeDerivative
    variable = velocity
  [../]

  [./momentum_convection]
    type = INSADMomentumAdvection
    variable = velocity
  [../]

  [./momentum_viscous]
    type = INSADMomentumViscous
    variable = velocity
  [../]

  [./momentum_pressure]
    type = INSADMomentumPressure
    variable = velocity
    p = p
    integrate_p_by_parts = true
  [../]

  [./momentum_supg]
    type = INSADMomentumSUPG
    variable = velocity
    velocity = velocity
  [../]

 [./temperature_advection]
   type = INSADEnergyAdvection
   variable = temperature
 [../]

 [temperature_time]
   type = INSADHeatConductionTimeDerivative
   variable = temperature
 []

 [./temperature_conduction]
   type = ADHeatConduction
   variable = temperature
   thermal_conductivity = 'k'
 [../]

  [temperature_supg]
    type = INSADEnergySUPG
    variable = temperature
    velocity = velocity
  []
[]

[BCs]
  [./no_slip]
    type = VectorFunctionDirichletBC
    variable = velocity
    boundary = 'bottom right left'
  [../]

  [./lid]
    type = VectorFunctionDirichletBC
    variable = velocity
    boundary = 'top'
    function_x = 'lid_function'
  [../]

  [./pressure_pin]
    type = DirichletBC
    variable = p
    boundary = 'pinned_node'
    value = 0
  [../]

  [./temperature_hot]
    type = DirichletBC
    variable = temperature
    boundary = 'bottom'
    value = 1
  [../]

  [./temperature_cold]
    type = DirichletBC
    variable = temperature
    boundary = 'top'
    value = 0
  [../]
[]

[Materials]
  [./const]
    type = ADGenericConstantMaterial
    prop_names = 'rho mu cp k'
    prop_values = '1  1  1  .01'
  [../]
  [ins_mat]
    type = INSADStabilized3Eqn
    velocity = velocity
    pressure = p
    temperature = temperature
  []
[]

[Functions]
  [./lid_function]
    # We pick a function that is exactly represented in the velocity
    # space so that the Dirichlet conditions are the same regardless
    # of the mesh spacing.
    type = ParsedFunction
    value = '4*x*(1-x)'
  [../]
[]

[Executioner]
  type = Transient
  solve_type = 'NEWTON'
  # Run for 100+ timesteps to reach steady state.
  num_steps = 5
  dt = .5
  dtmin = .5
  petsc_options_iname = '-pc_type -sub_pc_factor_levels -ksp_gmres_restart'
  petsc_options_value = 'asm      6                     200'
  line_search = 'none'
  nl_rel_tol = 1e-12
  nl_abs_tol =  1e-12
  nl_max_its = 6
[]

[Outputs]
  exodus = true
[]

Description
Input Parameters
Input Files

Install MOOSE

New Users

Examples and Tutorials

Application Usage

Physics and Syntax

Application Development

Framework Development

MOOSEDocs

Infrastructure

Questions

Information and Tools

INL Applications and Remote Access