SASFAnalyticalFluxBC

construction:Undocumented Class

The SASFAnalyticalFluxBC has not been documented. The content listed below should be used as a starting point for documenting the class, which includes the typical automatic documentation associated with a MooseObject; however, what is contained is ultimately determined by what is necessary to make the documentation clear for users.

Imposes a scalar flux boundary condition for the point source uncollided flux equation stabilized with the self-adjoint flux formalism.

Overview

Example Input File Syntax

Input Parameters

boundaryThe list of boundary IDs from the mesh where this object applies
C++ Type:std::vector<BoundaryName>
Controllable:No
Description:The list of boundary IDs from the mesh where this object applies
group_indexThe energy group index of the current angular flux.
C++ Type:unsigned int
Controllable:No
Description:The energy group index of the current angular flux.
group_sourceThe group-wise isotropic point source intensity.
C++ Type:std::vector<double>
Unit:(no unit assumed)
Controllable:No
Description:The group-wise isotropic point source intensity.
group_totalThe macroscopic total cross-sections for all energy groups.
C++ Type:std::vector<double>
Unit:(no unit assumed)
Controllable:No
Description:The macroscopic total cross-sections for all energy groups.
source_locationThe location of the point source.
C++ Type:libMesh::Point
Controllable:No
Description:The location of the point source.
variableThe name of the variable that this residual object operates on
C++ Type:NonlinearVariableName
Unit:(no unit assumed)
Controllable:No
Description:The name of the variable that this residual object operates on

Required Parameters

displacementsThe displacements
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:The displacements

Optional Parameters

absolute_value_vector_tagsThe tags for the vectors this residual object should fill with the absolute value of the residual contribution
C++ Type:std::vector<TagName>
Controllable:No
Description:The tags for the vectors this residual object should fill with the absolute value of the residual contribution
extra_matrix_tagsThe extra tags for the matrices this Kernel should fill
C++ Type:std::vector<TagName>
Controllable:No
Description:The extra tags for the matrices this Kernel should fill
extra_vector_tagsThe extra tags for the vectors this Kernel should fill
C++ Type:std::vector<TagName>
Controllable:No
Description:The extra tags for the vectors this Kernel should fill
matrix_tagssystemThe tag for the matrices this Kernel should fill
Default:system
C++ Type:MultiMooseEnum
Options:nontime, system
Controllable:No
Description:The tag for the matrices this Kernel should fill
vector_tagsnontimeThe tag for the vectors this Kernel should fill
Default:nontime
C++ Type:MultiMooseEnum
Options:nontime, time
Controllable:No
Description:The tag for the vectors this Kernel should fill

Contribution To Tagged Field Data Parameters

control_tagsAdds user-defined labels for accessing object parameters via control logic.
C++ Type:std::vector<std::string>
Controllable:No
Description:Adds user-defined labels for accessing object parameters via control logic.
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<AuxVariableName>
Unit:(no unit assumed)
Controllable:No
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
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
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<AuxVariableName>
Unit:(no unit assumed)
Controllable:No
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
Controllable:No
Description:The seed for the master random number generator
skip_execution_outside_variable_domainFalseWhether to skip execution of this boundary condition when the variable it applies to is not defined on the boundary. This can facilitate setups with moving variable domains and fixed boundaries. Note that the FEProblem boundary-restricted integrity checks will also need to be turned off if using this option
Default:False
C++ Type:bool
Controllable:No
Description:Whether to skip execution of this boundary condition when the variable it applies to is not defined on the boundary. This can facilitate setups with moving variable domains and fixed boundaries. Note that the FEProblem boundary-restricted integrity checks will also need to be turned off if using this option
use_displaced_meshFalseWhether or not this object should use the displaced mesh for computation. Note that in the case this is true but no displacements are provided in the Mesh block the undisplaced mesh will still be used.
Default:False
C++ Type:bool
Controllable:No
Description:Whether or not this object should use the displaced mesh for computation. Note that in the case this is true but no displacements are provided in the Mesh block the undisplaced mesh will still be used.

Advanced Parameters

prop_getter_suffixAn optional suffix parameter that can be appended to any attempt to retrieve/get material 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 attempt to retrieve/get material properties. The suffix will be prepended with a '_' character.
use_interpolated_stateFalseFor the old and older state use projected material properties interpolated at the quadrature points. To set up projection use the ProjectedStatefulMaterialStorageAction.
Default:False
C++ Type:bool
Controllable:No
Description:For the old and older state use projected material properties interpolated at the quadrature points. To set up projection use the ProjectedStatefulMaterialStorageAction.

Material Property Retrieval Parameters

Input Files

(examples/new_uncollided_method/3D_spatial_error/nsr_10_percent_1_octs.i)
(examples/new_uncollided_method/multiple_quadrants_2D/nsr_10_percent_1_quad.i)
(examples/new_uncollided_method/determining_zeta/nsr_10_percent_4_quad.i)
(examples/new_uncollided_method/spatial_convergence_2D/quads/spatial_convergence.i)
(examples/new_uncollided_method/misc_3D_tests/3D_shield_penetration.i)
(examples/new_uncollided_method/multiple_quadrants_2D/nsr_10_percent_3_quad.i)
(examples/new_uncollided_method/multiple_quadrants_2D/nsr_10_percent_4_quad.i)
(examples/new_uncollided_method/spatial_convergence_2D/tris/spatial_convergence.i)
(examples/new_uncollided_method/multiple_quadrants_2D/nsr_10_percent_2_quad.i)

(examples/new_uncollided_method/3D_spatial_error/nsr_10_percent_1_octs.i)

# A simple test case with a purely absorbing medium and a point source in the
# middle of the domain.

source = 1.0
xs = 0.0

[GlobalParams]
  source_location = '0.0 0.0 0.0'
[]

[Mesh]
  [domain]
    type = FileMeshGenerator
    file = 'nsr_10_one_octs_quads.e'
  []
  uniform_refine = 3
[]

[Variables]
  [UncollidedFlux]
    type = MooseVariable
    order = FIRST
    family = LAGRANGE
  []
[]

[AuxVariables]
  [UncollidedFluxAnal]
    type = MooseVariable
    order = FIRST
    family = LAGRANGE
  []
  [UncollidedError]
    type = MooseVariable
    order = FIRST
    family = LAGRANGE
  []
[]

[AuxKernels]
  [CompAnalyticalFlux]
    type = FunctionAux
    variable = UncollidedFluxAnal
    function = Exact
  []
  [SpatialError]
    type = ParsedAux
    variable = UncollidedError
    coupled_variables = 'UncollidedFlux UncollidedFluxAnal'
    expression = '100.0 * abs((UncollidedFlux - UncollidedFluxAnal) / UncollidedFluxAnal)'
  []
[]

[Kernels]
  [UncollidedFluxAdvection]
    type = SASFAdvection
    variable = UncollidedFlux
    group_index = 0
    transport_system = ''
  []
  [UncollidedFluxRemoval]
    type = SASFRemoval
    variable = UncollidedFlux
    group_index = 0
    transport_system = ''
  []
[]

[BCs]
  [UncollidedFluxVacuumBC]
    type = SASFVacuumBC
    variable = UncollidedFlux
    boundary = 'vacuum'
  []

  [UncollidedFluxSourceBC]
    type = SASFAnalyticalFluxBC
    variable = UncollidedFlux
    boundary = 'analytical_flux'
    group_index = 0
    group_source = ${source}
    group_total = ${xs}
  []
[]

[Materials]
  [Vacuum]
    type = AbsorbingNeutronicsMaterial
    transport_system = ''
    num_groups = 1
    group_total = ${xs}
  []
[]

[Functions]
  [Exact]
    type = ParsedFunction
    expression = '${source} * exp(-1.0 * ${xs} * sqrt(x * x + y * y + z * z)) / (4.0 * pi * (x * x + y * y + z * z))'
  []
[]

[Postprocessors]
  [L2Error]
    type = ElementL2Error
    function = Exact
    variable = UncollidedFlux
  []
  [h]
    type = AverageElementSize
  []
[]

[Executioner]
  type = Steady
  solve_type = PJFNK
  petsc_options_iname = '-pc_type -pc_hypre_type -ksp_gmres_restart'
  petsc_options_value = ' hypre    boomeramg      600'

  l_max_its = 50
  nl_abs_tol = 1e-12

  automatic_scaling = true
  off_diagonals_in_auto_scaling = true
  compute_scaling_once = false
[]

[Outputs]
  exodus = true
  csv = true
  execute_on = TIMESTEP_END
[]

(examples/new_uncollided_method/multiple_quadrants_2D/nsr_10_percent_1_quad.i)

# A simple test case with a purely absorbing medium and a point source in the
# middle of the domain.

source = 1.0
xs = 0.0

[GlobalParams]
  source_location = '0.0 0.0 0.0'
[]

[Mesh]
  [domain]
    type = FileMeshGenerator
    file = 'nsr_10_percent_1_quads.e'
  []
  uniform_refine = 0
[]

[Variables]
  [UncollidedFlux]
    type = MooseVariable
    order = FIRST
    family = LAGRANGE
  []
[]

#[DiracKernels]
#  [UncollidedFluxPointSource]
#    type = SASFPointSource
#    variable = UncollidedFlux
#    group_index = 0
#    transport_system = ''
#    group_source = 1.0
#  []
#[]

[Kernels]
  [UncollidedFluxAdvection]
    type = SASFAdvection
    variable = UncollidedFlux
    group_index = 0
    transport_system = ''
  []
  [UncollidedFluxRemoval]
    type = SASFRemoval
    variable = UncollidedFlux
    group_index = 0
    transport_system = ''
  []
[]

[BCs]
  [UncollidedFluxVacuumBC]
    type = SASFVacuumBC
    variable = UncollidedFlux
    boundary = 'vacuum'
  []

  [UncollidedFluxSourceBC]
    type = SASFAnalyticalFluxBC
    variable = UncollidedFlux
    boundary = 'analytical_flux'
    group_index = 0
    group_source = ${source}
    group_total = ${xs}
  []
[]

[Materials]
  [Vacuum]
    type = AbsorbingNeutronicsMaterial
    transport_system = ''
    num_groups = 1
    group_total = ${xs}
  []
[]

[Functions]
  [Exact]
    type = ParsedFunction
    expression = '${source} * exp(-1.0 * ${xs} * sqrt(x * x + y * y)) / (2.0 * pi * sqrt(x * x + y * y))'
  []
[]

[Postprocessors]
  [error]
    type = ElementL2Error
    function = Exact
    variable = UncollidedFlux
  []
  [h]
    type = AverageElementSize
  []
[]

[Executioner]
  type = Steady
  solve_type = PJFNK
  petsc_options_iname = '-pc_type -pc_factor_shift_type'
  petsc_options_value = ' lu       NONZERO'

  l_max_its = 50
  nl_abs_tol = 1e-12

  automatic_scaling = true
  off_diagonals_in_auto_scaling = true
  compute_scaling_once = false
[]

[Outputs]
  exodus = true
  csv = true
  execute_on = TIMESTEP_END
[]

(examples/new_uncollided_method/determining_zeta/nsr_10_percent_4_quad.i)

# A simple test case with a purely absorbing medium and a point source in the
# middle of the domain.

xs = 1e-6
eta = 2.0

[GlobalParams]
  source_location = '0.0 0.0 0.0'
[]

[Mesh]
  [domain]
    type = FileMeshGenerator
    file = 'nsr_10_percent_4_quads.e'
  []
  uniform_refine = 2
[]

[Variables]
  [UncollidedFlux]
    type = MooseVariable
    order = FIRST
    family = LAGRANGE
  []
[]

[Kernels]
  [UncollidedFluxAdvection]
    type = SASFAdvection
    variable = UncollidedFlux
    group_index = 0
    transport_system = ''
  []
  [UncollidedFluxRemoval]
    type = SASFRemoval
    variable = UncollidedFlux
    group_index = 0
    transport_system = ''
  []
[]

[BCs]
  [UncollidedFluxVacuumBC]
    type = SASFVacuumBC
    variable = UncollidedFlux
    boundary = 'vacuum'
  []

  [UncollidedFluxSourceBC]
    type = SASFAnalyticalFluxBC
    variable = UncollidedFlux
    boundary = 'analytical_flux'
    group_index = 0
    group_source = 1.0
    group_total = ${xs}
  []
[]

[Materials]
  [Vacuum]
    type = AbsorbingNeutronicsMaterial
    transport_system = ''
    num_groups = 1
    group_total = ${xs}
    saaf_eta = ${eta}
  []
[]

[Functions]
  [Exact]
    type = ParsedFunction
    expression = '(1.0 * exp(-1.0 * ${xs} * sqrt(x * x + y * y))) / (2.0 * pi * sqrt(x * x + y * y))'
  []
[]

[Postprocessors]
  [error]
    type = ElementL2Error
    function = Exact
    variable = UncollidedFlux
  []
  [h]
    type = AverageElementSize
  []
[]

[Executioner]
  type = Steady
  solve_type = PJFNK
  petsc_options_iname = '-pc_type'
  petsc_options_value = ' lu'
  #petsc_options_iname = '-pc_type -pc_hypre_type -ksp_gmres_restart'
  #petsc_options_value = ' hypre    boomeramg      100'

  l_max_its = 50
  nl_abs_tol = 1e-12
  nl_rel_tol = 1e-12

  automatic_scaling = true
  off_diagonals_in_auto_scaling = true
  compute_scaling_once = false
[]

[Outputs]
  exodus = true
  csv = true
  execute_on = TIMESTEP_END
[]

(examples/new_uncollided_method/spatial_convergence_2D/quads/spatial_convergence.i)

# A simple test case with a purely absorbing medium and a point source in the
# middle of the domain.

src_x = 0.0
src_y = 0.0
src_z = 0.0

shield_xs = 1e0
void_xs = 0.0

[GlobalParams]
  source_location = '${src_x} ${src_y} ${src_z}'
[]

[Mesh]
  [domain]
    type = FileMeshGenerator
    file = 'spatial_convergence_2_quad.e'
  []
[]

[AuxVariables]
  [AnalyticalFluxField]
    type = MooseVariable
    order = FIRST
    family = LAGRANGE
  []
  [UncollidedError]
    type = MooseVariable
    order = FIRST
    family = LAGRANGE
  []
[]

[AuxKernels]
  [CompAnalytical]
    type = FunctionAux
    variable = AnalyticalFluxField
    function = AnalyticalFlux
  []
  [SpatialError]
    type = ParsedAux
    variable = UncollidedError
    coupled_variables = 'UncollidedFlux AnalyticalFluxField'
    expression = 'abs(UncollidedFlux - AnalyticalFluxField) / AnalyticalFluxField'
  []
[]

[Variables]
  [UncollidedFlux]
    type = MooseVariable
    order = FIRST
    family = LAGRANGE
  []
[]

[Kernels]
  [UncollidedFluxAdvection]
    type = SASFAdvection
    variable = UncollidedFlux
    group_index = 0
    transport_system = ''
  []
  [UncollidedFluxRemoval]
    type = SASFRemoval
    variable = UncollidedFlux
    group_index = 0
    transport_system = ''
  []
[]

[BCs]
  [UncollidedFluxVacuumBC]
    type = SASFVacuumBC
    variable = UncollidedFlux
    boundary = 'vacuum'
  []
  [UncollidedFluxSourceBC]
    type = SASFAnalyticalFluxBC
    variable = UncollidedFlux
    boundary = 'analytical_flux'
    group_index = 0
    group_source = 1.0
    group_total = 0.0
  []
[]

[Materials]
  [Vacuum]
    type = AbsorbingNeutronicsMaterial
    transport_system = ''
    num_groups = 1
    group_total = '${void_xs}'
    block = 'empty'
    saaf_eta = 1.0
  []
  [Shield]
    type = AbsorbingNeutronicsMaterial
    transport_system = ''
    num_groups = 1
    group_total = '${shield_xs}'
    block = 'shield'
    saaf_eta = 1.0
  []
[]

[Executioner]
  type = Steady
  solve_type = PJFNK
  petsc_options_iname = '-pc_type -pc_factor_shift_type'
  petsc_options_value = ' lu       NONZERO'

  l_max_its = 50
  nl_abs_tol = 1e-12

  automatic_scaling = true
  off_diagonals_in_auto_scaling = true
  compute_scaling_once = false
[]

[Functions]
  [AnalyticalFlux]
    type = AxisymmetricPointScalarFlux
    num_dims = 2
    src_strength = 1.0
    src_location = '0 0 0'
    axisymmetric_radii = '2.0 4.0 6.0 8.0 20.0'
    axisymmetric_cross_sections = '${void_xs} ${shield_xs} ${void_xs} ${shield_xs} ${void_xs}'
  []
[]

[Postprocessors]
  [Error]
    type = ElementL2Error
    variable = UncollidedFlux
    function = AnalyticalFlux
  []
  [H]
    type = AverageElementMinSize
  []
[]

[Outputs]
  exodus = true
  csv = true
  execute_on = TIMESTEP_END
[]

(examples/new_uncollided_method/misc_3D_tests/3D_shield_penetration.i)

# A simple test case with a purely absorbing medium and a point source in the
# middle of the domain.

source = 1.0
xs = 0.0

src_x = 0.0
src_y = 0.0
src_z = 0.0

[GlobalParams]
  source_location = '${src_x} ${src_y} ${src_z}'
[]

[Mesh]
  [domain]
    type = FileMeshGenerator
    file = '3D_shield_penetration.e'
  []
  uniform_refine = 1
[]

[Adaptivity]
  marker = errorfrac
  steps = 15

  [Indicators]
    [error]
      type = GradientJumpIndicator
      variable = UncollidedFlux
      outputs = none
    []
  []

  [Markers]
    [errorfrac]
      type = ErrorFractionMarker
      indicator = error
      refine = 0.5
      coarsen = 0
      outputs = none
    []
  []
[]

[Variables]
  [UncollidedFlux]
    type = MooseVariable
    order = FIRST
    family = LAGRANGE
  []
[]

[Kernels]
  [UncollidedFluxAdvection]
    type = SASFAdvection
    variable = UncollidedFlux
    group_index = 0
    transport_system = ''
  []

  [UncollidedFluxRemoval]
    type = SASFRemoval
    variable = UncollidedFlux
    group_index = 0
    transport_system = ''
  []
[]

[BCs]
  [UncollidedFluxVacuumBC]
    type = SASFVacuumBC
    variable = UncollidedFlux
    boundary = 'vacuum'
  []

  [UncollidedFluxSourceBC]
    type = SASFAnalyticalFluxBC
    variable = UncollidedFlux
    boundary = 'analytical_flux'
    group_index = 0
    group_source = ${source}
    group_total = ${xs}
  []
[]

[Materials]
  [Vacuum]
    type = AbsorbingNeutronicsMaterial
    transport_system = ''
    num_groups = 1
    group_total = ${xs}
    block = empty
  []

  [Shield]
    type = AbsorbingNeutronicsMaterial
    transport_system = ''
    num_groups = 1
    group_total = 1.0
    block = shield
  []
[]

[Executioner]
  type = Steady
  solve_type = PJFNK
  petsc_options_iname = '-ksp_gmres_restart'
  petsc_options_value = ' 600'

  l_max_its = 50
  nl_abs_tol = 1e-12

  automatic_scaling = true
  off_diagonals_in_auto_scaling = true
  compute_scaling_once = false
[]

[Outputs]
  exodus = true
  execute_on = TIMESTEP_END
[]

(examples/new_uncollided_method/multiple_quadrants_2D/nsr_10_percent_3_quad.i)

# A simple test case with a purely absorbing medium and a point source in the
# middle of the domain.

source = 1.0
xs = 0.0

[GlobalParams]
  source_location = '0.0 0.0 0.0'
[]

[Mesh]
  [domain]
    type = FileMeshGenerator
    file = 'nsr_10_percent_3_quads.e'
  []
  uniform_refine = 0
[]

[Variables]
  [UncollidedFlux]
    type = MooseVariable
    order = FIRST
    family = LAGRANGE
  []
[]

#[DiracKernels]
#  [UncollidedFluxPointSource]
#    type = SASFPointSource
#    variable = UncollidedFlux
#    group_index = 0
#    transport_system = ''
#    group_source = 1.0
#  []
#[]

[Kernels]
  [UncollidedFluxAdvection]
    type = SASFAdvection
    variable = UncollidedFlux
    group_index = 0
    transport_system = ''
  []
  [UncollidedFluxRemoval]
    type = SASFRemoval
    variable = UncollidedFlux
    group_index = 0
    transport_system = ''
  []
[]

[BCs]
  [UncollidedFluxVacuumBC]
    type = SASFVacuumBC
    variable = UncollidedFlux
    boundary = 'vacuum'
  []

  [UncollidedFluxSourceBC]
    type = SASFAnalyticalFluxBC
    variable = UncollidedFlux
    boundary = 'analytical_flux'
    group_index = 0
    group_source = ${source}
    group_total = ${xs}
  []
[]

[Materials]
  [Vacuum]
    type = AbsorbingNeutronicsMaterial
    transport_system = ''
    num_groups = 1
    group_total = ${xs}
  []
[]

[Functions]
  [Exact]
    type = ParsedFunction
    expression = '${source} * exp(-1.0 * ${xs} * sqrt(x * x + y * y)) / (2.0 * pi * sqrt(x * x + y * y))'
  []
[]

[Postprocessors]
  [error]
    type = ElementL2Error
    function = Exact
    variable = UncollidedFlux
  []
  [h]
    type = AverageElementSize
  []
[]

[Executioner]
  type = Steady
  solve_type = PJFNK
  petsc_options_iname = '-pc_type -pc_factor_shift_type'
  petsc_options_value = ' lu       NONZERO'

  l_max_its = 50
  nl_abs_tol = 1e-12

  automatic_scaling = true
  off_diagonals_in_auto_scaling = true
  compute_scaling_once = false
[]

[Outputs]
  exodus = true
  csv = true
  execute_on = TIMESTEP_END
[]

(examples/new_uncollided_method/multiple_quadrants_2D/nsr_10_percent_4_quad.i)

# A simple test case with a purely absorbing medium and a point source in the
# middle of the domain.

source = 1.0
xs = 0.0

[GlobalParams]
  source_location = '0.0 0.0 0.0'
[]

[Mesh]
  [domain]
    type = FileMeshGenerator
    file = 'nsr_10_percent_4_quads.e'
  []
  uniform_refine = 0
[]

[Variables]
  [UncollidedFlux]
    type = MooseVariable
    order = FIRST
    family = LAGRANGE
  []
[]

#[DiracKernels]
#  [UncollidedFluxPointSource]
#    type = SASFPointSource
#    variable = UncollidedFlux
#    group_index = 0
#    transport_system = ''
#    group_source = 1.0
#  []
#[]

[Kernels]
  [UncollidedFluxAdvection]
    type = SASFAdvection
    variable = UncollidedFlux
    group_index = 0
    transport_system = ''
  []
  [UncollidedFluxRemoval]
    type = SASFRemoval
    variable = UncollidedFlux
    group_index = 0
    transport_system = ''
  []
[]

[BCs]
  [UncollidedFluxVacuumBC]
    type = SASFVacuumBC
    variable = UncollidedFlux
    boundary = 'vacuum'
  []

  [UncollidedFluxSourceBC]
    type = SASFAnalyticalFluxBC
    variable = UncollidedFlux
    boundary = 'analytical_flux'
    group_index = 0
    group_source = ${source}
    group_total = ${xs}
  []
[]

[Materials]
  [Vacuum]
    type = AbsorbingNeutronicsMaterial
    transport_system = ''
    num_groups = 1
    group_total = ${xs}
  []
[]

[Functions]
  [Exact]
    type = ParsedFunction
    expression = '${source} * exp(-1.0 * ${xs} * sqrt(x * x + y * y)) / (2.0 * pi * sqrt(x * x + y * y))'
  []
[]

[Postprocessors]
  [error]
    type = ElementL2Error
    function = Exact
    variable = UncollidedFlux
  []
  [h]
    type = AverageElementSize
  []
[]

[Executioner]
  type = Steady
  solve_type = PJFNK
  petsc_options_iname = '-pc_type -pc_factor_shift_type'
  petsc_options_value = ' lu       NONZERO'

  l_max_its = 50
  nl_abs_tol = 1e-12

  automatic_scaling = true
  off_diagonals_in_auto_scaling = true
  compute_scaling_once = false
[]

[Outputs]
  exodus = true
  csv = true
  execute_on = TIMESTEP_END
[]

(examples/new_uncollided_method/spatial_convergence_2D/tris/spatial_convergence.i)

# A simple test case with a purely absorbing medium and a point source in the
# middle of the domain.

src_x = 0.0
src_y = 0.0
src_z = 0.0

shield_xs = 1.0
void_xs = 0.0

[GlobalParams]
  source_location = '${src_x} ${src_y} ${src_z}'
[]

[Mesh]
  [domain]
    type = FileMeshGenerator
    file = 'spatial_convergence_0_tris.e'
  []
[]

[AuxVariables]
  [AnalyticalFluxField]
    type = MooseVariable
    order = FIRST
    family = LAGRANGE
  []
  [UncollidedError]
    type = MooseVariable
    order = FIRST
    family = LAGRANGE
  []
[]

[AuxKernels]
  [CompAnalytical]
    type = FunctionAux
    variable = AnalyticalFluxField
    function = AnalyticalFlux
  []
  [SpatialError]
    type = ParsedAux
    variable = UncollidedError
    coupled_variables = 'UncollidedFlux AnalyticalFluxField'
    expression = 'abs(UncollidedFlux - AnalyticalFluxField) / AnalyticalFluxField'
  []
[]

[Variables]
  [UncollidedFlux]
    type = MooseVariable
    order = FIRST
    family = LAGRANGE
  []
[]

[Kernels]
  [UncollidedFluxAdvection]
    type = SASFAdvection
    variable = UncollidedFlux
    group_index = 0
    transport_system = ''
  []
  [UncollidedFluxRemoval]
    type = SASFRemoval
    variable = UncollidedFlux
    group_index = 0
    transport_system = ''
  []
[]

[BCs]
  [UncollidedFluxVacuumBC]
    type = SASFVacuumBC
    variable = UncollidedFlux
    boundary = 'vacuum'
  []
  [UncollidedFluxSourceBC]
    type = SASFAnalyticalFluxBC
    variable = UncollidedFlux
    boundary = 'analytical_flux'
    group_index = 0
    group_source = 1.0
    group_total = 0.0
  []
[]

[Materials]
  [Vacuum]
    type = AbsorbingNeutronicsMaterial
    transport_system = ''
    num_groups = 1
    group_total = '${void_xs}'
    block = 'empty'
    saaf_eta = 1.0
  []
  [Shield]
    type = AbsorbingNeutronicsMaterial
    transport_system = ''
    num_groups = 1
    group_total = '${shield_xs}'
    block = 'shield'
    saaf_eta = 1.0
  []
[]

[Executioner]
  type = Steady
  solve_type = PJFNK
  petsc_options_iname = '-pc_type -pc_factor_shift_type'
  petsc_options_value = ' lu       NONZERO'

  l_max_its = 50
  nl_abs_tol = 1e-12

  automatic_scaling = true
  off_diagonals_in_auto_scaling = true
  compute_scaling_once = false
[]

[Functions]
  [AnalyticalFlux]
    type = AxisymmetricPointScalarFlux
    num_dims = 2
    src_strength = 1.0
    src_location = '0 0 0'
    axisymmetric_radii = '2.0 4.0 6.0 8.0 20.0'
    axisymmetric_cross_sections = '${void_xs} ${shield_xs} ${void_xs} ${shield_xs} ${void_xs}'
  []
[]

[Postprocessors]
  [Error]
    type = ElementL2Error
    variable = UncollidedFlux
    function = AnalyticalFlux
  []
  [H]
    type = AverageElementMinSize
  []
[]

[Outputs]
  exodus = true
  csv = true
  execute_on = TIMESTEP_END
[]

(examples/new_uncollided_method/multiple_quadrants_2D/nsr_10_percent_2_quad.i)

# A simple test case with a purely absorbing medium and a point source in the
# middle of the domain.

source = 1.0
xs = 0.0

[GlobalParams]
  source_location = '0.0 0.0 0.0'
[]

[Mesh]
  [domain]
    type = FileMeshGenerator
    file = 'nsr_10_percent_2_quads.e'
  []
  uniform_refine = 0
[]

[Variables]
  [UncollidedFlux]
    type = MooseVariable
    order = FIRST
    family = LAGRANGE
  []
[]

#[DiracKernels]
#  [UncollidedFluxPointSource]
#    type = SASFPointSource
#    variable = UncollidedFlux
#    group_index = 0
#    transport_system = ''
#    group_source = 1.0
#  []
#[]

[Kernels]
  [UncollidedFluxAdvection]
    type = SASFAdvection
    variable = UncollidedFlux
    group_index = 0
    transport_system = ''
  []
  [UncollidedFluxRemoval]
    type = SASFRemoval
    variable = UncollidedFlux
    group_index = 0
    transport_system = ''
  []
[]

[BCs]
  [UncollidedFluxVacuumBC]
    type = SASFVacuumBC
    variable = UncollidedFlux
    boundary = 'vacuum'
  []

  [UncollidedFluxSourceBC]
    type = SASFAnalyticalFluxBC
    variable = UncollidedFlux
    boundary = 'analytical_flux'
    group_index = 0
    group_source = ${source}
    group_total = ${xs}
  []
[]

[Materials]
  [Vacuum]
    type = AbsorbingNeutronicsMaterial
    transport_system = ''
    num_groups = 1
    group_total = ${xs}
  []
[]

[Functions]
  [Exact]
    type = ParsedFunction
    expression = '${source} * exp(-1.0 * ${xs} * sqrt(x * x + y * y)) / (2.0 * pi * sqrt(x * x + y * y))'
  []
[]

[Postprocessors]
  [error]
    type = ElementL2Error
    function = Exact
    variable = UncollidedFlux
  []
  [h]
    type = AverageElementSize
  []
[]

[Executioner]
  type = Steady
  solve_type = PJFNK
  petsc_options_iname = '-pc_type -pc_factor_shift_type'
  petsc_options_value = ' lu       NONZERO'

  l_max_its = 50
  nl_abs_tol = 1e-12

  automatic_scaling = true
  off_diagonals_in_auto_scaling = true
  compute_scaling_once = false
[]

[Outputs]
  exodus = true
  csv = true
  execute_on = TIMESTEP_END
[]

Overview
Example Input File Syntax
Input Parameters
Input Files