FDTallyGradAux

Description

FDTallyGradAux approximates tally gradients using forward finite differences between the current element and its neighbors. The approach used is based on the derivative approximation presented in Stolte and Tsvetkov (2023):

$(1)var element = document.getElementById("moose-equation-b18fedac-41de-4294-b317-10e340d866c6");katex.render(" \\vec{\\nabla}u(\\vec{x}_{i}) \\approx Y_{i}^{-1}\\sum_{i'} \\frac{\\vec{x}_{i'} - \\vec{x}_{i}}{||\\vec{x}_{i'} - \\vec{x}_{i}||}\\frac{u(\\vec{x}_{i'}) - u(\\vec{x}_{i})}{||\\vec{x}_{i'} - \\vec{x}_{i}||}\\text{,}", element, {displayMode:true,throwOnError:false});$ $(2)var element = document.getElementById("moose-equation-ac68f828-9981-4b09-9fc3-ef3dca22fe5e");katex.render(" Y_{i} = \\sum_{i'} (\\vec{x}_{i'} - \\vec{x}_{i})\\otimes (\\vec{x}_{i'} - \\vec{x}_{i}) \\text{,}", element, {displayMode:true,throwOnError:false});$ where $var element = document.getElementById("moose-equation-0d82bec9-ac96-4615-a7d4-405e9013794d");katex.render("i", element, {displayMode:false,throwOnError:false});$ indicates the current element, $var element = document.getElementById("moose-equation-29fe7a6f-6667-46c8-8856-fe4492a653a9");katex.render("i'", element, {displayMode:false,throwOnError:false});$ is a neighboring element, $var element = document.getElementById("moose-equation-7de8c4b2-fa96-4c7e-855c-4b1985f087ac");katex.render("\\vec{x}", element, {displayMode:false,throwOnError:false});$ is an element's centroid, and $var element = document.getElementById("moose-equation-b4c5bef5-d2d0-45fb-bece-df6eacf17825");katex.render("u", element, {displayMode:false,throwOnError:false});$ is the tally field. A tally score must be specified, and if any external filter bins have been added through the use of the filter system ext_filter_bin index should be provided.

Example Input Syntax

This example showcases how FDTallyGradAux can be used to approximate the gradient of kappa_fission:

[AuxKernels<<<{"href": "../../syntax/AuxKernels/index.html"}>>>]
  [comp_grad_kappa_fission]
    type = FDTallyGradAux<<<{"description": "An auxkernel which approximates tally gradients at element centroids using forward finite differences.", "href": "FDTallyGradAux.html"}>>>
    variable<<<{"description": "The name of the variable that this object applies to"}>>> = grad_kappa_fission
    score<<<{"description": "The tally score this auxkernel should approximate the gradient of."}>>> = 'kappa_fission'
  []
[]

Input Parameters

scoreThe tally score this auxkernel should approximate the gradient of.
C++ Type:MooseEnum
Options:heating, heating_local, kappa_fission, fission_q_prompt, fission_q_recoverable, damage_energy, flux, H3_production, total, absorption, scatter, nu_scatter, fission, nu_fission, inverse_velocity
Controllable:No
Description:The tally score this auxkernel should approximate the gradient of.
variableThe name of the variable that this object applies to
C++ Type:AuxVariableName
Unit:(no unit assumed)
Controllable:No
Description:The name of the variable that this object applies to

Required Parameters

blockThe list of blocks (ids or names) that this object will be applied
C++ Type:std::vector<SubdomainName>
Controllable:No
Description:The list of blocks (ids or names) that this object will be applied
boundaryThe list of boundaries (ids or names) from the mesh where this object applies
C++ Type:std::vector<BoundaryName>
Controllable:No
Description:The list of boundaries (ids or names) from the mesh where this object applies
check_boundary_restrictedTrueWhether to check for multiple element sides on the boundary in the case of a boundary restricted, element aux variable. Setting this to false will allow contribution to a single element's elemental value(s) from multiple boundary sides on the same element (example: when the restricted boundary exists on two or more sides of an element, such as at a corner of a mesh
Default:True
C++ Type:bool
Controllable:No
Description:Whether to check for multiple element sides on the boundary in the case of a boundary restricted, element aux variable. Setting this to false will allow contribution to a single element's elemental value(s) from multiple boundary sides on the same element (example: when the restricted boundary exists on two or more sides of an element, such as at a corner of a mesh
execute_onLINEAR TIMESTEP_ENDThe 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:LINEAR TIMESTEP_END
C++ Type:ExecFlagEnum
Options: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, PRE_DISPLACE
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.
ext_filter_bin0The filter bin for the case where any filters are added to this tally with [Filters] (bin indices start at 0). This parameter should be specified if you wish to extract the relative error of a different non-spatial tally bin.
Default:0
C++ Type:unsigned int
Controllable:No
Description:The filter bin for the case where any filters are added to this tally with [Filters] (bin indices start at 0). This parameter should be specified if you wish to extract the relative error of a different non-spatial tally bin.

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.
seed0The seed for the master random number generator
Default:0
C++ Type:unsigned int
Controllable:No
Description:The seed for the master random number generator
use_displaced_meshFalseWhether or not this object should use the displaced mesh for computation. Note that in the case this is true but no displacements are provided in the Mesh block the undisplaced mesh will still be used.
Default:False
C++ Type:bool
Controllable:No
Description:Whether or not this object should use the displaced mesh for computation. Note that in the case this is true but no displacements are provided in the Mesh block the undisplaced mesh will still be used.

Advanced Parameters

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

References

K. N. Stolte and P. V. Tsvetkov. χ-MeRA: computationally efficient adaptive mesh refinement of monte carlo mesh based tallies. Annals of Nuclear Energy, 182:109617, 2023. doi:https://doi.org/10.1016/j.anucene.2022.109617.

@article{stolte,
    author = "Stolte, K. N. and Tsvetkov, P. V.",
    title = "{$\chi$-MeRA}: Computationally Efficient Adaptive Mesh Refinement of Monte Carlo Mesh Based Tallies",
    journal = "Annals of Nuclear Energy",
    volume = "182",
    pages = "109617",
    year = "2023",
    doi = "https://doi.org/10.1016/j.anucene.2022.109617"
}

(cardinal/test/tests/neutronics/tally_grad/finite_diff/openmc.i)

[Mesh]
  [sphere]
    type = FileMeshGenerator
    file = ../../meshes/sphere.e
  []
  [solid1]
    type = SubdomainIDGenerator
    input = sphere
    subdomain_id = '100'
  []

  allow_renumbering = false
  parallel_type = replicated
[]

[AuxVariables]
  [grad_kappa_fission]
    type = VectorMooseVariable
    family = MONOMIAL_VEC
    order = CONSTANT
  []
[]

[AuxKernels]
  [comp_grad_kappa_fission]
    type = FDTallyGradAux
    variable = grad_kappa_fission
    score = 'kappa_fission'
  []
[]

[Problem]
  type = OpenMCCellAverageProblem
  temperature_blocks = '100'
  initial_properties = xml
  verbose = true
  cell_level = 0
  normalize_by_global_tally = false

  power = 100.0

  [Tallies]
    [Mesh]
      type = MeshTally
      score = 'kappa_fission'
    []
  []
[]

[Executioner]
  type = Steady
[]

[Outputs]
  execute_on = final
  exodus = true
  hide = 'temp cell_instance cell_id kappa_fission'
[]

Description
Example Input Syntax
Input Parameters
References