FXFluxBC

Sets a flux boundary condition, evaluated using a FunctionSeries instance. This does not fix the flux, but rather 'strongly encourages' flux agreement by penalizing the differences through contributions to the residual.

Description

This BC provides a strongly encouraged FE-based Neumann boundary condition. It subclasses FunctionNeumannBC to perform the actual work. The only differences in FXFluxBC are:

it ensures that the provided Function is a subclass of FunctionSeries
it configures the provided FunctionSeries to use memoization (caching) for FX evaluations to improve performance

Example Input File Syntax

Listing 1: Example use of FXFluxBC

[BCs]
  [./interface_value]
    type = FXValueBC
    variable = m
    boundary = right
    function = FX_Basis_Value_Main
  [../]
  [./interface_flux]
    type = FXFluxBC
    boundary = right
    variable = m
    function = FX_Basis_Flux_Main
  [../]
[]

/opt/civet/build_0/moose/modules/functional_expansion_tools/examples/2D_interface/main.i

# Basic example coupling a master and sub app at an interface in a 2D model.
# The master app provides a flux term to the sub app via Functional Expansions, which then performs
# its calculations.  The sub app's interface conditions, both value and flux, are transferred back
# to the master app
[Mesh]
  type = GeneratedMesh
  dim = 2
  xmin = 0.0
  xmax = 0.4
  nx = 6
  ymin = 0.0
  ymax = 10.0
  ny = 20
[]

[Variables]
  [./m]
  [../]
[]

[Kernels]
  [./diff_m]
    type = HeatConduction
    variable = m
  [../]
  [./time_diff_m]
    type = HeatConductionTimeDerivative
    variable = m
  [../]
  [./source_m]
    type = BodyForce
    variable = m
    value = 100
  [../]
[]

[Materials]
  [./Impervium]
    type = GenericConstantMaterial
    prop_names =  'thermal_conductivity specific_heat density'
    prop_values = '0.00001              50.0          100.0' # W/(cm K), J/(g K), g/cm^3
  [../]
[]

[ICs]
  [./start_m]
    type = ConstantIC
    value = 2
    variable = m
  [../]
[]

[BCs]
  [./interface_value]
    type = FXValueBC
    variable = m
    boundary = right
    function = FX_Basis_Value_Main
  [../]
  [./interface_flux]
    type = FXFluxBC
    boundary = right
    variable = m
    function = FX_Basis_Flux_Main
  [../]
[]

[Functions]
  [./FX_Basis_Value_Main]
    type = FunctionSeries
    series_type = Cartesian
    orders = '4'
    physical_bounds = '0.0 10'
    y = Legendre
  [../]
  [./FX_Basis_Flux_Main]
    type = FunctionSeries
    series_type = Cartesian
    orders = '5'
    physical_bounds = '0.0 10'
    y = Legendre
  [../]
[]

[UserObjects]
  [./FX_Flux_UserObject_Main]
    type = FXBoundaryFluxUserObject
    function = FX_Basis_Flux_Main
    variable = m
    boundary = right
    diffusivity = thermal_conductivity
  [../]
[]

[Postprocessors]
  [./average_interface_value]
    type = SideAverageValue
    variable = m
    boundary = right
  [../]
  [./total_flux]
    type = SideFluxIntegral
    variable = m
    boundary = right
    diffusivity = thermal_conductivity
  [../]
  [./picard_iterations]
    type = NumPicardIterations
    execute_on = 'initial timestep_end'
  [../]
[]

[Executioner]
  type = Transient
  num_steps = 10
  dt = 1.0
  solve_type = PJFNK
  petsc_options_iname = '-pc_type -pc_hypre_type'
  petsc_options_value = 'hypre boomeramg'
  picard_max_its = 30
  nl_rel_tol = 1e-8
  nl_abs_tol = 1e-9
  picard_rel_tol = 1e-8
  picard_abs_tol = 1e-9
[]

[Outputs]
  exodus = true
[]

[MultiApps]
  [./FXTransferApp]
    type = TransientMultiApp
    input_files = sub.i
    sub_cycling = true
  [../]
[]

[Transfers]
  [./FluxToSub]
    type = MultiAppFXTransfer
    direction = to_multiapp
    multi_app = FXTransferApp
    this_app_object_name = FX_Flux_UserObject_Main
    multi_app_object_name = FX_Basis_Flux_Sub
  [../]
  [./ValueToMe]
    type = MultiAppFXTransfer
    direction = from_multiapp
    multi_app = FXTransferApp
    this_app_object_name = FX_Basis_Value_Main
    multi_app_object_name = FX_Value_UserObject_Sub
  [../]
  [./FluxToMe]
    type = MultiAppFXTransfer
    direction = from_multiapp
    multi_app = FXTransferApp
    this_app_object_name = FX_Basis_Flux_Main
    multi_app_object_name = FX_Flux_UserObject_Sub
  [../]
[]

Input Parameters

boundaryThe list of boundary IDs from the mesh where this boundary condition applies
C++ Type:std::vector
Options:
Description:The list of boundary IDs from the mesh where this boundary condition applies
functionThe function.
C++ Type:FunctionName
Options:
Description:The function.
variableThe name of the variable that this boundary condition applies to
C++ Type:NonlinearVariableName
Options:
Description:The name of the variable that this boundary condition applies to

Required Parameters

displacementsThe displacements
C++ Type:std::vector
Options:
Description:The displacements

Optional Parameters

control_tagsAdds user-defined labels for accessing object parameters via control logic.
C++ Type:std::vector
Options:
Description:Adds user-defined labels for accessing object parameters via control logic.
diag_save_inThe name of auxiliary variables to save this BC'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
Options:
Description:The name of auxiliary variables to save this BC'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 BC'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
Options:
Description:The name of auxiliary variables to save this BC'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
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
Options:
Description:The extra tags for the vectors this Kernel should fill
matrix_tagssystemThe tag for the matrices this Kernel should fill
Default:system
C++ Type:MultiMooseEnum
Options:nontime system
Description:The tag for the matrices this Kernel should fill
vector_tagsnontimeThe tag for the vectors this Kernel should fill
Default:nontime
C++ Type:MultiMooseEnum
Options:nontime time
Description:The tag for the vectors this Kernel should fill

Tagging Parameters

Input Files

modules/functional_expansion_tools/test/tests/standard_use/interface_sub.i
modules/functional_expansion_tools/examples/2D_interface_different_submesh/sub.i
modules/functional_expansion_tools/examples/2D_interface/main.i
modules/functional_expansion_tools/examples/2D_interface/sub.i
modules/functional_expansion_tools/test/tests/errors/bc_flux_bad_function.i
modules/functional_expansion_tools/test/tests/standard_use/interface_coupled.i
modules/functional_expansion_tools/examples/2D_interface_different_submesh/main.i
modules/functional_expansion_tools/examples/2D_interface_no_material/main.i
modules/functional_expansion_tools/examples/2D_interface_no_material/sub.i

modules/functional_expansion_tools/test/tests/standard_use/interface_sub.i

[Mesh]
  type = GeneratedMesh
  dim = 2
  xmin = 0.4
  xmax = 2.4
  nx = 30
  ymin = 0.0
  ymax = 10.0
  ny = 20
[]

[Variables]
  [./s]
  [../]
[]

[Kernels]
  [./diff_s]
    type = Diffusion
    variable = s
  [../]
  [./time_diff_s]
    type = TimeDerivative
    variable = s
  [../]
[]

[ICs]
  [./start_s]
    type = ConstantIC
    value = 2
    variable = s
  [../]
[]

[BCs]
  [./bottom]
    type = DirichletBC
    variable = s
    boundary = bottom
    value = 0.1
  [../]
  [./interface_flux]
    type = FXFluxBC
    boundary = left
    variable = s
    function = FX_Basis_Flux_Sub
  [../]
[]

[Functions]
  [./FX_Basis_Value_Sub]
    type = FunctionSeries
    series_type = Cartesian
    orders = '4'
    physical_bounds = '0.0 10'
    y = Legendre
  [../]
  [./FX_Basis_Flux_Sub]
    type = FunctionSeries
    series_type = Cartesian
    orders = '5'
    physical_bounds = '0.0 10'
    y = Legendre
  [../]
[]

[UserObjects]
  [./FX_Value_UserObject_Sub]
    type = FXBoundaryValueUserObject
    function = FX_Basis_Value_Sub
    variable = s
    boundary = left
  [../]
  [./FX_Flux_UserObject_Sub]
    type = FXBoundaryFluxUserObject
    function = FX_Basis_Flux_Sub
    variable = s
    boundary = left
    diffusivity = 1.0
  [../]
[]

[Executioner]
  type = Transient
  num_steps = 4
  dt = 1.0
  solve_type = PJFNK
  petsc_options_iname = '-pc_type -pc_hypre_type'
  petsc_options_value = 'hypre boomeramg'
[]

modules/functional_expansion_tools/examples/2D_interface_different_submesh/sub.i

# Derived from the example '2D_interface' with the following differences:
#
#   1) The number of y divisions in the sub app is not the same as the master app
#   2) The subapp mesh is skewed in y
#   3) The Functional Expansion order for the flux term was increased to 7
[Mesh]
  type = GeneratedMesh
  dim = 2
  xmin = 0.4
  xmax = 2.4
  nx = 30
  ymin = 0.0
  ymax = 10.0
  ny = 23
  bias_y = 1.2
[]

[Variables]
  [./s]
  [../]
[]

[Kernels]
  [./diff_s]
    type = HeatConduction
    variable = s
  [../]
  [./time_diff_s]
    type = HeatConductionTimeDerivative
    variable = s
  [../]
[]

[Materials]
  [./Unobtanium]
    type = GenericConstantMaterial
    prop_names =  'thermal_conductivity specific_heat density'
    prop_values = '1.0                  1.0           1.0' # W/(cm K), J/(g K), g/cm^3
  [../]
[]

[ICs]
  [./start_s]
    type = ConstantIC
    value = 2
    variable = s
  [../]
[]

[BCs]
  [./bottom]
    type = DirichletBC
    variable = s
    boundary = bottom
    value = 0.1
  [../]
  [./interface_flux]
    type = FXFluxBC
    boundary = left
    variable = s
    function = FX_Basis_Flux_Sub
  [../]
[]

[Functions]
  [./FX_Basis_Value_Sub]
    type = FunctionSeries
    series_type = Cartesian
    orders = '4'
    physical_bounds = '0.0 10'
    y = Legendre
  [../]
  [./FX_Basis_Flux_Sub]
    type = FunctionSeries
    series_type = Cartesian
    orders = '7'
    physical_bounds = '0.0 10'
    y = Legendre
  [../]
[]

[UserObjects]
  [./FX_Value_UserObject_Sub]
    type = FXBoundaryValueUserObject
    function = FX_Basis_Value_Sub
    variable = s
    boundary = left
  [../]
  [./FX_Flux_UserObject_Sub]
    type = FXBoundaryFluxUserObject
    function = FX_Basis_Flux_Sub
    variable = s
    boundary = left
    diffusivity = thermal_conductivity
  [../]
[]

[Executioner]
  type = Transient
  num_steps = 10
  dt = 1.0
  solve_type = PJFNK
  petsc_options_iname = '-pc_type -pc_hypre_type'
  petsc_options_value = 'hypre boomeramg'
[]

modules/functional_expansion_tools/examples/2D_interface/main.i

# Basic example coupling a master and sub app at an interface in a 2D model.
# The master app provides a flux term to the sub app via Functional Expansions, which then performs
# its calculations.  The sub app's interface conditions, both value and flux, are transferred back
# to the master app
[Mesh]
  type = GeneratedMesh
  dim = 2
  xmin = 0.0
  xmax = 0.4
  nx = 6
  ymin = 0.0
  ymax = 10.0
  ny = 20
[]

[Variables]
  [./m]
  [../]
[]

[Kernels]
  [./diff_m]
    type = HeatConduction
    variable = m
  [../]
  [./time_diff_m]
    type = HeatConductionTimeDerivative
    variable = m
  [../]
  [./source_m]
    type = BodyForce
    variable = m
    value = 100
  [../]
[]

[Materials]
  [./Impervium]
    type = GenericConstantMaterial
    prop_names =  'thermal_conductivity specific_heat density'
    prop_values = '0.00001              50.0          100.0' # W/(cm K), J/(g K), g/cm^3
  [../]
[]

[ICs]
  [./start_m]
    type = ConstantIC
    value = 2
    variable = m
  [../]
[]

[BCs]
  [./interface_value]
    type = FXValueBC
    variable = m
    boundary = right
    function = FX_Basis_Value_Main
  [../]
  [./interface_flux]
    type = FXFluxBC
    boundary = right
    variable = m
    function = FX_Basis_Flux_Main
  [../]
[]

[Functions]
  [./FX_Basis_Value_Main]
    type = FunctionSeries
    series_type = Cartesian
    orders = '4'
    physical_bounds = '0.0 10'
    y = Legendre
  [../]
  [./FX_Basis_Flux_Main]
    type = FunctionSeries
    series_type = Cartesian
    orders = '5'
    physical_bounds = '0.0 10'
    y = Legendre
  [../]
[]

[UserObjects]
  [./FX_Flux_UserObject_Main]
    type = FXBoundaryFluxUserObject
    function = FX_Basis_Flux_Main
    variable = m
    boundary = right
    diffusivity = thermal_conductivity
  [../]
[]

[Postprocessors]
  [./average_interface_value]
    type = SideAverageValue
    variable = m
    boundary = right
  [../]
  [./total_flux]
    type = SideFluxIntegral
    variable = m
    boundary = right
    diffusivity = thermal_conductivity
  [../]
  [./picard_iterations]
    type = NumPicardIterations
    execute_on = 'initial timestep_end'
  [../]
[]

[Executioner]
  type = Transient
  num_steps = 10
  dt = 1.0
  solve_type = PJFNK
  petsc_options_iname = '-pc_type -pc_hypre_type'
  petsc_options_value = 'hypre boomeramg'
  picard_max_its = 30
  nl_rel_tol = 1e-8
  nl_abs_tol = 1e-9
  picard_rel_tol = 1e-8
  picard_abs_tol = 1e-9
[]

[Outputs]
  exodus = true
[]

[MultiApps]
  [./FXTransferApp]
    type = TransientMultiApp
    input_files = sub.i
    sub_cycling = true
  [../]
[]

[Transfers]
  [./FluxToSub]
    type = MultiAppFXTransfer
    direction = to_multiapp
    multi_app = FXTransferApp
    this_app_object_name = FX_Flux_UserObject_Main
    multi_app_object_name = FX_Basis_Flux_Sub
  [../]
  [./ValueToMe]
    type = MultiAppFXTransfer
    direction = from_multiapp
    multi_app = FXTransferApp
    this_app_object_name = FX_Basis_Value_Main
    multi_app_object_name = FX_Value_UserObject_Sub
  [../]
  [./FluxToMe]
    type = MultiAppFXTransfer
    direction = from_multiapp
    multi_app = FXTransferApp
    this_app_object_name = FX_Basis_Flux_Main
    multi_app_object_name = FX_Flux_UserObject_Sub
  [../]
[]

modules/functional_expansion_tools/examples/2D_interface/sub.i

# Basic example coupling a master and sub app at an interface in a 2D model.
# The master app provides a flux term to the sub app via Functional Expansions, which then performs
# its calculations.  The sub app's interface conditions, both value and flux, are transferred back
# to the master app
[Mesh]
  type = GeneratedMesh
  dim = 2
  xmin = 0.4
  xmax = 2.4
  nx = 30
  ymin = 0.0
  ymax = 10.0
  ny = 20
[]

[Variables]
  [./s]
  [../]
[]

[Kernels]
  [./diff_s]
    type = HeatConduction
    variable = s
  [../]
  [./time_diff_s]
    type = HeatConductionTimeDerivative
    variable = s
  [../]
[]

[Materials]
  [./Unobtanium]
    type = GenericConstantMaterial
    prop_names =  'thermal_conductivity specific_heat density'
    prop_values = '1.0                  1.0           1.0' # W/(cm K), J/(g K), g/cm^3
  [../]
[]

[ICs]
  [./start_s]
    type = ConstantIC
    value = 2
    variable = s
  [../]
[]

[BCs]
  [./bottom]
    type = DirichletBC
    variable = s
    boundary = bottom
    value = 0.1
  [../]
  [./interface_flux]
    type = FXFluxBC
    boundary = left
    variable = s
    function = FX_Basis_Flux_Sub
  [../]
[]

[Functions]
  [./FX_Basis_Value_Sub]
    type = FunctionSeries
    series_type = Cartesian
    orders = '4'
    physical_bounds = '0.0 10'
    y = Legendre
  [../]
  [./FX_Basis_Flux_Sub]
    type = FunctionSeries
    series_type = Cartesian
    orders = '5'
    physical_bounds = '0.0 10'
    y = Legendre
  [../]
[]

[UserObjects]
  [./FX_Value_UserObject_Sub]
    type = FXBoundaryValueUserObject
    function = FX_Basis_Value_Sub
    variable = s
    boundary = left
  [../]
  [./FX_Flux_UserObject_Sub]
    type = FXBoundaryFluxUserObject
    function = FX_Basis_Flux_Sub
    variable = s
    boundary = left
    diffusivity = thermal_conductivity
  [../]
[]

[Executioner]
  type = Transient
  num_steps = 10
  dt = 1.0
  solve_type = PJFNK
  petsc_options_iname = '-pc_type -pc_hypre_type'
  petsc_options_value = 'hypre boomeramg'
[]

modules/functional_expansion_tools/test/tests/errors/bc_flux_bad_function.i

[Mesh]
  type = GeneratedMesh
  dim = 1
[]

[Variables]
  [./v]
  [../]
[]

[BCs]
  [./this_could_be_bad]
    type = FXFluxBC
    boundary = right
    function = const
    variable = v
  [../]
[]

[Functions]
  [./const]
    type = ConstantFunction
    value = -1
  [../]
[]

[Executioner]
  type = Steady
[]

[Problem]
  solve = false
[]

modules/functional_expansion_tools/test/tests/standard_use/interface_coupled.i

[Mesh]
  type = GeneratedMesh
  dim = 2
  xmin = 0.0
  xmax = 0.4
  nx = 6
  ymin = 0.0
  ymax = 10.0
  ny = 20
[]

[Variables]
  [./m]
  [../]
[]

[Kernels]
  [./diff_m]
    type = Diffusion
    variable = m
  [../]
  [./time_diff_m]
    type = TimeDerivative
    variable = m
  [../]
  [./source_m]
    type = BodyForce
    variable = m
    value = 100
  [../]
[]

[ICs]
  [./start_m]
    type = ConstantIC
    value = 2
    variable = m
  [../]
[]

[BCs]
  [./interface_value]
    type = FXValueBC
    variable = m
    boundary = right
    function = FX_Basis_Value_Main
  [../]
  [./interface_flux]
    type = FXFluxBC
    boundary = right
    variable = m
    function = FX_Basis_Flux_Main
  [../]
[]

[Functions]
  [./FX_Basis_Value_Main]
    type = FunctionSeries
    series_type = Cartesian
    orders = '4'
    physical_bounds = '0.0 10'
    y = Legendre
  [../]
  [./FX_Basis_Flux_Main]
    type = FunctionSeries
    series_type = Cartesian
    orders = '5'
    physical_bounds = '0.0 10'
    y = Legendre
  [../]
[]

[UserObjects]
  [./FX_Flux_UserObject_Main]
    type = FXBoundaryFluxUserObject
    function = FX_Basis_Flux_Main
    variable = m
    boundary = right
    diffusivity = 0.1
  [../]
[]

[Postprocessors]
  [./average_interface_value]
    type = SideAverageValue
    variable = m
    boundary = right
  [../]
  [./total_flux]
    type = SideFluxIntegral
    variable = m
    boundary = right
    diffusivity = 0.1
  [../]
  [./picard_iterations]
    type = NumPicardIterations
    execute_on = 'initial timestep_end'
  [../]
[]

[Executioner]
  type = Transient
  num_steps = 4
  dt = 1.0
  solve_type = PJFNK
  petsc_options_iname = '-pc_type -pc_hypre_type'
  petsc_options_value = 'hypre boomeramg'
  picard_max_its = 30
  nl_rel_tol = 1e-8
  nl_abs_tol = 1e-9
  picard_rel_tol = 1e-8
  picard_abs_tol = 1e-9
[]

[Outputs]
  exodus = true
[]

[MultiApps]
  [./FXTransferApp]
    type = TransientMultiApp
    input_files = interface_sub.i
    sub_cycling = true
  [../]
[]

[Transfers]
  [./FluxToSub]
    type = MultiAppFXTransfer
    direction = to_multiapp
    multi_app = FXTransferApp
    this_app_object_name = FX_Flux_UserObject_Main
    multi_app_object_name = FX_Basis_Flux_Sub
  [../]
  [./ValueToMe]
    type = MultiAppFXTransfer
    direction = from_multiapp
    multi_app = FXTransferApp
    this_app_object_name = FX_Basis_Value_Main
    multi_app_object_name = FX_Value_UserObject_Sub
  [../]
  [./FluxToMe]
    type = MultiAppFXTransfer
    direction = from_multiapp
    multi_app = FXTransferApp
    this_app_object_name = FX_Basis_Flux_Main
    multi_app_object_name = FX_Flux_UserObject_Sub
  [../]
[]

modules/functional_expansion_tools/examples/2D_interface_different_submesh/main.i

# Derived from the example '2D_interface' with the following differences:
#
#   1) The number of y divisions in the sub app is not the same as the master app
#   2) The subapp mesh is skewed in y
#   3) The Functional Expansion order for the flux term was increased to 7
[Mesh]
  type = GeneratedMesh
  dim = 2
  xmin = 0.0
  xmax = 0.4
  nx = 6
  ymin = 0.0
  ymax = 10.0
  ny = 20
[]

[Variables]
  [./m]
  [../]
[]

[Kernels]
  [./diff_m]
    type = HeatConduction
    variable = m
  [../]
  [./time_diff_m]
    type = HeatConductionTimeDerivative
    variable = m
  [../]
  [./source_m]
    type = BodyForce
    variable = m
    value = 100
  [../]
[]

[Materials]
  [./Impervium]
    type = GenericConstantMaterial
    prop_names =  'thermal_conductivity specific_heat density'
    prop_values = '0.00001              50.0          100.0' # W/(cm K), J/(g K), g/cm^3
  [../]
[]

[ICs]
  [./start_m]
    type = ConstantIC
    value = 2
    variable = m
  [../]
[]

[BCs]
  [./interface_value]
    type = FXValueBC
    variable = m
    boundary = right
    function = FX_Basis_Value_Main
  [../]
  [./interface_flux]
    type = FXFluxBC
    boundary = right
    variable = m
    function = FX_Basis_Flux_Main
  [../]
[]

[Functions]
  [./FX_Basis_Value_Main]
    type = FunctionSeries
    series_type = Cartesian
    orders = '4'
    physical_bounds = '0.0 10'
    y = Legendre
  [../]
  [./FX_Basis_Flux_Main]
    type = FunctionSeries
    series_type = Cartesian
    orders = '7'
    physical_bounds = '0.0 10'
    y = Legendre
  [../]
[]

[UserObjects]
  [./FX_Flux_UserObject_Main]
    type = FXBoundaryFluxUserObject
    function = FX_Basis_Flux_Main
    variable = m
    boundary = right
    diffusivity = thermal_conductivity
  [../]
[]

[Postprocessors]
  [./average_interface_value]
    type = SideAverageValue
    variable = m
    boundary = right
  [../]
  [./total_flux]
    type = SideFluxIntegral
    variable = m
    boundary = right
    diffusivity = thermal_conductivity
  [../]
  [./picard_iterations]
    type = NumPicardIterations
    execute_on = 'initial timestep_end'
  [../]
[]

[Executioner]
  type = Transient
  num_steps = 10
  dt = 1.0
  solve_type = PJFNK
  petsc_options_iname = '-pc_type -pc_hypre_type'
  petsc_options_value = 'hypre boomeramg'
  picard_max_its = 30
  nl_rel_tol = 1e-8
  nl_abs_tol = 1e-9
  picard_rel_tol = 1e-8
  picard_abs_tol = 1e-9
[]

[Outputs]
  exodus = true
[]

[MultiApps]
  [./FXTransferApp]
    type = TransientMultiApp
    input_files = sub.i
    sub_cycling = true
  [../]
[]

[Transfers]
  [./FluxToSub]
    type = MultiAppFXTransfer
    direction = to_multiapp
    multi_app = FXTransferApp
    this_app_object_name = FX_Flux_UserObject_Main
    multi_app_object_name = FX_Basis_Flux_Sub
  [../]
  [./ValueToMe]
    type = MultiAppFXTransfer
    direction = from_multiapp
    multi_app = FXTransferApp
    this_app_object_name = FX_Basis_Value_Main
    multi_app_object_name = FX_Value_UserObject_Sub
  [../]
  [./FluxToMe]
    type = MultiAppFXTransfer
    direction = from_multiapp
    multi_app = FXTransferApp
    this_app_object_name = FX_Basis_Flux_Main
    multi_app_object_name = FX_Flux_UserObject_Sub
  [../]
[]

modules/functional_expansion_tools/examples/2D_interface_no_material/main.i

# Derived from the example '2D_interface' with the following differences:
#
#   1) No materials are used
[Mesh]
  type = GeneratedMesh
  dim = 2
  xmin = 0.0
  xmax = 0.4
  nx = 6
  ymin = 0.0
  ymax = 10.0
  ny = 20
[]

[Variables]
  [./m]
  [../]
[]

[Kernels]
  [./diff_m]
    type = Diffusion
    variable = m
  [../]
  [./time_diff_m]
    type = TimeDerivative
    variable = m
  [../]
  [./source_m]
    type = BodyForce
    variable = m
    value = 100
  [../]
[]

[ICs]
  [./start_m]
    type = ConstantIC
    value = 2
    variable = m
  [../]
[]

[BCs]
  [./interface_value]
    type = FXValueBC
    variable = m
    boundary = right
    function = FX_Basis_Value_Main
  [../]
  [./interface_flux]
    type = FXFluxBC
    boundary = right
    variable = m
    function = FX_Basis_Flux_Main
  [../]
[]

[Functions]
  [./FX_Basis_Value_Main]
    type = FunctionSeries
    series_type = Cartesian
    orders = '4'
    physical_bounds = '0.0 10'
    y = Legendre
  [../]
  [./FX_Basis_Flux_Main]
    type = FunctionSeries
    series_type = Cartesian
    orders = '5'
    physical_bounds = '0.0 10'
    y = Legendre
  [../]
[]

[UserObjects]
  [./FX_Flux_UserObject_Main]
    type = FXBoundaryFluxUserObject
    function = FX_Basis_Flux_Main
    variable = m
    boundary = right
    diffusivity = 0.1
  [../]
[]

[Postprocessors]
  [./average_interface_value]
    type = SideAverageValue
    variable = m
    boundary = right
  [../]
  [./total_flux]
    type = SideFluxIntegral
    variable = m
    boundary = right
    diffusivity = 0.1
  [../]
  [./picard_iterations]
    type = NumPicardIterations
    execute_on = 'initial timestep_end'
  [../]
[]

[Executioner]
  type = Transient
  num_steps = 10
  dt = 1.0
  solve_type = PJFNK
  petsc_options_iname = '-pc_type -pc_hypre_type'
  petsc_options_value = 'hypre boomeramg'
  picard_max_its = 30
  nl_rel_tol = 1e-8
  nl_abs_tol = 1e-9
  picard_rel_tol = 1e-8
  picard_abs_tol = 1e-9
[]

[Outputs]
  exodus = true
[]

[MultiApps]
  [./FXTransferApp]
    type = TransientMultiApp
    input_files = sub.i
    sub_cycling = true
  [../]
[]

[Transfers]
  [./FluxToSub]
    type = MultiAppFXTransfer
    direction = to_multiapp
    multi_app = FXTransferApp
    this_app_object_name = FX_Flux_UserObject_Main
    multi_app_object_name = FX_Basis_Flux_Sub
  [../]
  [./ValueToMe]
    type = MultiAppFXTransfer
    direction = from_multiapp
    multi_app = FXTransferApp
    this_app_object_name = FX_Basis_Value_Main
    multi_app_object_name = FX_Value_UserObject_Sub
  [../]
  [./FluxToMe]
    type = MultiAppFXTransfer
    direction = from_multiapp
    multi_app = FXTransferApp
    this_app_object_name = FX_Basis_Flux_Main
    multi_app_object_name = FX_Flux_UserObject_Sub
  [../]
[]

modules/functional_expansion_tools/examples/2D_interface_no_material/sub.i

# Derived from the example '2D_interface' with the following differences:
#
#   1) No materials are used
[Mesh]
  type = GeneratedMesh
  dim = 2
  xmin = 0.4
  xmax = 2.4
  nx = 30
  ymin = 0.0
  ymax = 10.0
  ny = 20
[]

[Variables]
  [./s]
  [../]
[]

[Kernels]
  [./diff_s]
    type = Diffusion
    variable = s
  [../]
  [./time_diff_s]
    type = TimeDerivative
    variable = s
  [../]
[]

[ICs]
  [./start_s]
    type = ConstantIC
    value = 2
    variable = s
  [../]
[]

[BCs]
  [./bottom]
    type = DirichletBC
    variable = s
    boundary = bottom
    value = 0.1
  [../]
  [./interface_flux]
    type = FXFluxBC
    boundary = left
    variable = s
    function = FX_Basis_Flux_Sub
  [../]
[]

[Functions]
  [./FX_Basis_Value_Sub]
    type = FunctionSeries
    series_type = Cartesian
    orders = '4'
    physical_bounds = '0.0 10'
    y = Legendre
  [../]
  [./FX_Basis_Flux_Sub]
    type = FunctionSeries
    series_type = Cartesian
    orders = '5'
    physical_bounds = '0.0 10'
    y = Legendre
  [../]
[]

[UserObjects]
  [./FX_Value_UserObject_Sub]
    type = FXBoundaryValueUserObject
    function = FX_Basis_Value_Sub
    variable = s
    boundary = left
  [../]
  [./FX_Flux_UserObject_Sub]
    type = FXBoundaryFluxUserObject
    function = FX_Basis_Flux_Sub
    variable = s
    boundary = left
    diffusivity = 1.0
  [../]
[]

[Executioner]
  type = Transient
  num_steps = 10
  dt = 1.0
  solve_type = PJFNK
  petsc_options_iname = '-pc_type -pc_hypre_type'
  petsc_options_value = 'hypre boomeramg'
[]

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