PercolationUserObject

Enhanced FeatureFloodCount that provides a list of clusters that touch a specified boundary

This object performs the work of FeatureFloodCount, which it inherits from. The flood_entity_type is hardcoded to ELEMENTAL. After the flood counting pass another pass is made over the internal datastructure containing the cluster IDs per element. Clusters in all elements adjacent to at least one of the selected boundaries or to an element that has been cut by XFEM are flagged as providing a percolated path to a surface.

This object is to be used in conjunction with PercolationAux which assigns the percolation status to an AuxVariable.

Input Parameters

boundariesSet of free surfaces. Clusters touching any of these are set as percolated.
C++ Type:std::vector<BoundaryName>
Controllable:No
Description:Set of free surfaces. Clusters touching any of these are set as percolated.
variableThe variable(s) for which to find connected regions of interests, i.e. "features".
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:The variable(s) for which to find connected regions of interests, i.e. "features".

Required Parameters

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
compute_halo_mapsFalseInstruct the Postprocessor to communicate proper halo information to all ranks
Default:False
C++ Type:bool
Controllable:No
Description:Instruct the Postprocessor to communicate proper halo information to all ranks
compute_var_to_feature_mapFalseInstruct the Postprocessor to compute the active vars to features map
Default:False
C++ Type:bool
Controllable:No
Description:Instruct the Postprocessor to compute the active vars to features map
connecting_thresholdThe threshold for which an existing feature may be extended (defaults to "threshold")
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:The threshold for which an existing feature may be extended (defaults to "threshold")
enable_var_coloringFalseInstruct the Postprocessor to populate the variable index map.
Default:False
C++ Type:bool
Controllable:No
Description:Instruct the Postprocessor to populate the variable index map.
secondary_percolation_boundariesPaired boundaries with "primaryary_percolation_boundaries" parameter
C++ Type:std::vector<BoundaryName>
Controllable:No
Description:Paired boundaries with "primaryary_percolation_boundaries" parameter
specified_boundariesAn optional list of boundaries; if supplied, each feature is checked to determine whether it intersects any of the specified boundaries in this list.
C++ Type:std::vector<BoundaryName>
Controllable:No
Description:An optional list of boundaries; if supplied, each feature is checked to determine whether it intersects any of the specified boundaries in this list.
threshold0.5The threshold value for which a new feature may be started
Default:0.5
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:The threshold value for which a new feature may be started
use_less_than_threshold_comparisonTrueControls whether features are defined to be less than or greater than the threshold value.
Default:True
C++ Type:bool
Controllable:No
Description:Controls whether features are defined to be less than or greater than the threshold value.
use_xfemFalseIf true, percolation to cracks inserted by XFEM will be considered.
Default:False
C++ Type:bool
Controllable:No
Description:If true, percolation to cracks inserted by XFEM will be considered.

Optional Parameters

allow_duplicate_execution_on_initialFalseIn the case where this UserObject is depended upon by an initial condition, allow it to be executed twice during the initial setup (once before the IC and again after mesh adaptivity (if applicable).
Default:False
C++ Type:bool
Controllable:No
Description:In the case where this UserObject is depended upon by an initial condition, allow it to be executed twice during the initial setup (once before the IC and again after mesh adaptivity (if applicable).
execute_onTIMESTEP_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:TIMESTEP_END
C++ Type:ExecFlagEnum
Options:XFEM_MARK, NONE, INITIAL, LINEAR, NONLINEAR_CONVERGENCE, NONLINEAR, POSTCHECK, TIMESTEP_END, TIMESTEP_BEGIN, MULTIAPP_FIXED_POINT_END, MULTIAPP_FIXED_POINT_BEGIN, FINAL, CUSTOM, TRANSFER
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.
execution_order_group0Execution order groups are executed in increasing order (e.g., the lowest number is executed first). Note that negative group numbers may be used to execute groups before the default (0) group. Please refer to the user object documentation for ordering of user object execution within a group.
Default:0
C++ Type:int
Controllable:No
Description:Execution order groups are executed in increasing order (e.g., the lowest number is executed first). Note that negative group numbers may be used to execute groups before the default (0) group. Please refer to the user object documentation for ordering of user object execution within a group.
force_postauxFalseForces the UserObject to be executed in POSTAUX
Default:False
C++ Type:bool
Controllable:No
Description:Forces the UserObject to be executed in POSTAUX
force_preauxFalseForces the UserObject to be executed in PREAUX
Default:False
C++ Type:bool
Controllable:No
Description:Forces the UserObject to be executed in PREAUX
force_preicFalseForces the UserObject to be executed in PREIC during initial setup
Default:False
C++ Type:bool
Controllable:No
Description:Forces the UserObject to be executed in PREIC during initial setup

Execution Scheduling Parameters

condense_map_infoFalseDetermines whether we condense all the node values when in multimap mode (default: false)
Default:False
C++ Type:bool
Controllable:No
Description:Determines whether we condense all the node values when in multimap mode (default: false)
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.
outputsVector of output names where you would like to restrict the output of variables(s) associated with this object
C++ Type:std::vector<OutputName>
Controllable:No
Description:Vector of output names where you would like to restrict the output of variables(s) associated with this object
primary_percolation_boundariesA list of boundaries used in conjunction with the corresponding "secondary_percolation_boundaries" parameter for determining if a feature creates a path connecting any pair of boundaries
C++ Type:std::vector<BoundaryName>
Controllable:No
Description:A list of boundaries used in conjunction with the corresponding "secondary_percolation_boundaries" parameter for determining if a feature creates a path connecting any pair of boundaries
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.
use_global_numberingTrueDetermine whether or not global numbers are used to label features on multiple maps (default: true)
Default:True
C++ Type:bool
Controllable:No
Description:Determine whether or not global numbers are used to label features on multiple maps (default: true)
use_single_mapTrueDetermine whether information is tracked per coupled variable or consolidated into one (default: true)
Default:True
C++ Type:bool
Controllable:No
Description:Determine whether information is tracked per coupled variable or consolidated into one (default: true)

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

(test/tests/sifgrs/uo2/percolation.i)
(test/tests/sifgrs/uo2/percolation_xfem.i)
(test/tests/percolation/percolation_test.i)
(test/tests/sifgrs/uo2/ad_percolation.i)
(test/tests/sifgrs/uo2/ad_percolation_xfem.i)

(test/tests/sifgrs/uo2/percolation.i)

# This test is to verify that the optional check for a path to a free surface for gas release works correctly.
# When the optional percolation AuxVariable is supplied to Sifgrs, gas release is not allowed unless
# that variable is > 0.5 locally. The PercolationUserObject checks whether each position is connected
# to a free surface and sets the AuxVariable accordingly.

# In this test, the gas released should be nearly the same as the sifgrs_second_stage test.

[Mesh]
  [mesh]
    type = FileMeshGenerator
    file = 1hex8_10mm_cube.e
  []
  [free1]
    type = SideSetsAroundSubdomainGenerator
    new_boundary = free1
    normal = '1 0 0'
    block = 1
    input = mesh
  []
[]

[Functions]
  [Temp_func]
    type = ParsedFunction
    expression = '1400'
  []
  [Fiss_func]
    type = ParsedFunction
    expression = '1.e19'
  []
[]

[Variables]
  [T]
    initial_condition = 1400
  []
[]

[AuxVariables]
  [fission_rate]
  []
  [GBCoverage]
    order = CONSTANT
    family = MONOMIAL
  []
  # percolation AuxVariables
  [open_coverage]
    order = CONSTANT
    family = MONOMIAL
  []
  [open_threshold]
    order = CONSTANT
    family = MONOMIAL
  []
  [open]
    order = CONSTANT
    family = MONOMIAL
  []
  [cluster]
    order = CONSTANT
    family = MONOMIAL
  []
  [percolated]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[Kernels]
  [heat]
    type = HeatConduction
    variable = T
    diffusion_coefficient = 1
  []
[]

[AuxKernels]
  [fissionrate]
    type = FissionRateGeneral
    fission_rate_formulation = GENERIC
    variable = fission_rate
    value = 1
    fission_rate_function = Fiss_func
    execute_on = 'initial timestep_begin'
  []
  [frcvrg]
    type = MaterialRealAux
    variable = GBCoverage
    property = GBCoverage
    execute_on = 'initial linear'
  []
  # percolation auxkernels
  [open_coverage]
    type = MaterialRealAux
    variable = open_coverage
    property = GBCoverage
  []
  [open_threshold]
    type = MaterialRealAux
    variable = open_threshold
    property = sat_coverage
  []
  [open]
    type = ParsedAux
    variable = open
    coupled_variables = 'open_coverage open_threshold'
    expression = 'open_coverage-open_threshold'
  []
  [cluster]
    type = FeatureFloodCountAux
    variable = cluster
    execute_on = 'timestep_begin'
    field_display = UNIQUE_REGION
    flood_counter = percolate
  []
  [percolated]
    type = PercolationAux
    variable = percolated
    execute_on = 'timestep_begin'
    percolation = percolate
  []
[]

[BCs]
  [bottom_T]
    type = FunctionDirichletBC
    variable = T
    function = Temp_func
    boundary = 1
  []
[]

[Materials]
  [fission_gas_behavior]
    type = UO2Sifgrs
    block = 1
    temperature = T
    fission_rate = fission_rate
    percolation_to_surface = percolated
  []
[]

[Executioner]
  type = Transient
  solve_type = 'PJFNK'

  l_tol = 1e-4
  nl_abs_tol = 1e-5
  nl_rel_tol = 1e-5
  start_time = 0.0
  num_steps = 50
  dt = 1e6
  end_time = 5e7
[]

[Postprocessors]
  [fis_gas_generated]
    type = ElementIntegralFisGasGeneratedSifgrs
  []
  [fis_gas_released]
    type = ElementIntegralFisGasReleasedSifgrs
  []
[]

[UserObjects]
  [percolate]
    type = PercolationUserObject
    execute_on = 'timestep_begin'
    boundaries = 'free1'
    variable = open
    threshold = 0.0
  []
[]

[Outputs]
  exodus = true
[]

(test/tests/sifgrs/uo2/percolation_xfem.i)

# This is to test gas release through elements that are cut by XFEM. A 2D domain is
# used and the LineSegmentCutUserObject is used to insert a crack from the right edge
# of the domain inward toward the left edge. Because of the boundary conditions on temperature,
# gas would not normally be released to the free surface on the left side, but
# with the crack present gas release occurs.

[GlobalParams]
  density = 10970
  order = FIRST
  family = LAGRANGE
  energy_per_fission = 3.2e-11
[]

[Mesh]
  [mesh]
    type = GeneratedMeshGenerator
    dim = 2
    xmin = 0
    xmax = 0.005
    ymin = 0
    ymax = 0.005
    nx = 5
    ny = 5
  []
  [create_block2]
    type = RenameBlockGenerator
    input = mesh
    old_block = 0
    new_block = 2
  []
  [free1]
    type = SideSetsAroundSubdomainGenerator
    new_boundary = free1
    normal = '1 0 0'
    block = 2
    input = create_block2
  []
  [subdomain1]
    type = SubdomainBoundingBoxGenerator
    bottom_left = '0 0 0'
    top_right = '0.005 0.005 0'
    block_id = 2
    input = free1
  []
[]

#Create a notch in the mesh using XFEM
[XFEM]
  qrule = volfrac
  output_cut_plane = true
[]

[UserObjects]
  [line_seg_cut_uo]
    type = LineSegmentCutUserObject
    cut_data = '0.005 0.0025 0.001 0.0025'
    time_start_cut = 0.0
    time_end_cut = 0.0
  []
[]

[Variables]
  [temp]
    initial_condition = 673.
  []
[]

[AuxVariables]
  [grain_radius]
    block = 2
    initial_condition = 5.e-06
  []
  [gas_gen_3]
    order = CONSTANT
    family = MONOMIAL
    block = 2
  []
  [GBCoverage]
    order = CONSTANT
    family = MONOMIAL
  []
  [thermal_conductivity]
    order = CONSTANT
    family = MONOMIAL
    block = 2
  []
  [burnup]
    block = 2
  []
  [fission_rate]
    block = 2
  []

  # percolation variables
  [open_coverage]
    order = CONSTANT
    family = MONOMIAL
  []
  [open_threshold]
    order = CONSTANT
    family = MONOMIAL
  []
  [open]
    order = CONSTANT
    family = MONOMIAL
  []
  [cluster]
    order = CONSTANT
    family = MONOMIAL
  []
  [percolated]
    order = CONSTANT
    family = MONOMIAL
  []
[]

# Define functions to control power and boundary conditions
[Functions]
  [power_history]
    type = PiecewiseLinear
    x = '0.   10800.  1.0e+8'
    y = '0.   25.     25.   '
    scale_factor = 1000.
  []
  [pressure_ramp]
    type = PiecewiseLinear
    x = '0.     1.0e+8'
    y = '25.     25.'
    scale_factor = 1.0e+6
  []
[]

[Kernels]
  [heat] # gradient term in heat conduction equation
    type = HeatConduction
    variable = temp
  []
  [heat_ie] # time term in heat conduction equation
    type = HeatConductionTimeDerivative
    variable = temp
  []
  [heat_source] # source term in heat conduction equation
    type = NeutronHeatSource
    variable = temp
    block = 2
    fission_rate = fission_rate # coupling to the fission_rate aux variable
  []
[]

# Define auxilliary kernels for each of the aux variables
[AuxKernels]
  [fggen]
    type = MaterialRealAux
    variable = gas_gen_3
    property = gas_concentration_generated_total
  []
  [fractcov]
    type = MaterialRealAux
    variable = GBCoverage
    property = GBCoverage
    block = 2
  []
  [fuel_conductivity]
    type = MaterialRealAux
    variable = thermal_conductivity
    property = thermal_conductivity
  []
  [brnp]
    type = BurnupAux
    variable = burnup
    block = 2
    fission_rate = fission_rate
    molecular_weight = 0.270
  []
  [frate]
    type = FissionRateGeneral
    fission_rate_formulation = GENERIC
    variable = fission_rate
    block = 2
    value = 5.e+14
    fission_rate_function = power_history
  []

  # percolation auxkernels
  [open_coverage]
    type = MaterialRealAux
    variable = open_coverage
    property = GBCoverage
  []
  [open_threshold]
    type = MaterialRealAux
    variable = open_threshold
    property = 0.3 #GB coverage at which trijunction network is percolated
  []
  [open]
    type = ParsedAux
    variable = open
    coupled_variables = 'open_coverage open_threshold'
    expression = 'open_coverage-open_threshold'
  []
  [cluster]
    type = FeatureFloodCountAux
    variable = cluster
    execute_on = 'timestep_begin'
    field_display = UNIQUE_REGION
    flood_counter = percolate
  []
  [percolated]
    type = PercolationAux
    variable = percolated
    execute_on = 'timestep_begin'
    percolation = percolate
  []
[]

# Define boundary conditions
[BCs]
  [imposed_ext_temp]
    type = DirichletBC
    boundary = right
    variable = temp
    value = 673.
  []
  # insulate the top and bottom of this pellet
  [top_pellet]
    variable = temp
    value = 0.
    type = NeumannBC
    boundary = top
  []
  [bottom_pellet]
    variable = temp
    value = 0.
    type = NeumannBC
    boundary = bottom
  []
  [left_pellet]
    variable = temp
    value = 0.
    type = NeumannBC
    boundary = left
  []
[]

# Define material behavior models and input material property data
[Materials]
  [fuel_thermal]
    type = HeatConductionMaterial
    block = 2
    thermal_conductivity = 3.
    specific_heat = 400.
  []
  [fuel_density]
    type = ParsedMaterial
    block = 2
    property_name = density
    expression = 10970
  []
  [fission_gas_release_and_swelling]
    type = UO2Sifgrs
    block = 2
    diff_coeff_option = TURNBULL_D1_D2
    transient_option = MICROCRACKING
    res_param_option = HETEROGENEOUS_WHITE
    temperature = temp
    fission_rate = fission_rate
    burnup = burnup
    initial_porosity = 0.
    percolation_to_surface = percolated
  []
[]

[Dampers]
  [limitT]
    type = MaxIncrement
    max_increment = 50.
    variable = temp
  []
[]

[Executioner]
  type = Transient
  solve_type = 'PJFNK'

  petsc_options = '-ksp_gmres_modifiedgramschmidt'
  petsc_options_iname = '-ksp_gmres_restart -pc_type  -pc_composite_pcs -sub_0_pc_hypre_type -sub_0_pc_hypre_boomeramg_max_iter -sub_0_pc_hypre_boomeramg_grid_sweeps_all -sub_1_sub_pc_type -pc_composite_type -ksp_type -mat_mffd_type'
  petsc_options_value = '201                 composite hypre,asm         boomeramg            2                                  2                                         lu                 multiplicative     fgmres    ds'

  line_search = 'none'

  # controls for linear iterations
  l_max_its = 100
  l_tol = 1.0e-06

  # controls for nonlinear iterations
  nl_max_its = 10
  nl_rel_tol = 1.0e-4
  nl_abs_tol = 1.0e-8

  # time control
  start_time = 0.

  end_time = 1.0e+8
  num_steps = 5000
  dtmax = 1.0e+06
  dtmin = 1.0

  [TimeStepper]
    type = IterationAdaptiveDT
    dt = 1.0
    timestep_limiting_function = power_history
    max_function_change = 3000.
    force_step_every_function_point = true
  []
  [Quadrature]
    order = THIRD
  []
[]

[UserObjects]
  [percolate]
    type = PercolationUserObject
    execute_on = 'timestep_begin'
    boundaries = 'free1'
    variable = open
    threshold = 0.0
    use_xfem = true
  []
[]

# Define postprocessors (some are required as specified above; others are optional; many others are available)
[Postprocessors]
  [ave_burnup_EAV]
    type = ElementAverageValue
    block = 2
    variable = burnup
  []
  [fis_gas_released]
    type = ElementIntegralFisGasReleasedSifgrs
    block = 2
  []
[]

# Define output file(s)
[Outputs]
  time_step_interval =  1
  csv = true
  exodus = true
  color = true
  print_linear_residuals = true
  [console]
    type = Console
    max_rows = 25
    output_linear = true
  []
[]

(test/tests/percolation/percolation_test.i)

#
# Percolation test
#
# This test is designed to test the combination of the FeatureFloodCount and
# PercolationUserObject user objects and the output of their data through
# PercolationAux.
#
# The percolation system takes a set of clusters detected using the
# FeatureFloodCount object and tags all clusters touching a given boundary (or set
# of boundaries).
#
# This system can be used for the simulation of Stage 3 fission gas release,
# where grain boundary gas is only released if a percolated path all the way to
# the pellet surface (or internal crack surfaces) exists.
#
# This test cannot be run in recover mode because running recover requires at
# least three timesteps yet this test has only two timesteps.
#
[Mesh]
  [mesh]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 20
    ny = 20
  []
[]

[AuxVariables]
  [open]
    order = CONSTANT
    family = MONOMIAL
  []
  [cluster]
    order = CONSTANT
    family = MONOMIAL
  []
  [percolated]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[Variables]
  [c]
    [InitialCondition]
      # set up a cluster distrubution usinga  simple sin/cos function
      type = FunctionIC
      function = (sin(4+x*8-y)*cos(y*10+1.5*x))^2
    []
  []
[]

[AuxKernels]
  [open]
    type = ParsedAux
    execute_on = 'TIMESTEP_BEGIN'
    variable = open
    coupled_variables = c
    expression = c
  []
  [cluster]
    type = FeatureFloodCountAux
    variable = cluster
    execute_on = 'TIMESTEP_BEGIN'
    field_display = UNIQUE_REGION
    flood_counter = percolate
  []
  [percolated]
    type = PercolationAux
    variable = percolated
    # The percolated AuxVariable is initialized at the beginning of the timestep.
    execute_on = 'TIMESTEP_BEGIN'
    percolation = percolate
  []
[]

[UserObjects]
  [percolate]
    type = PercolationUserObject
    execute_on = 'TIMESTEP_BEGIN'
    boundaries = 'top left'
    variable = open
    threshold = 0.1
  []
[]

[Executioner]
  type = Transient
  dt = 1e-4
  num_steps = 2
[]

[Problem]
  kernel_coverage_check = false
[]

[Outputs]
  exodus = true
  show = percolated
  print_linear_residuals = false
[]

(test/tests/sifgrs/uo2/ad_percolation.i)

# This test is to verify that the optional check for a path to a free surface for gas release works correctly.
# When the optional percolation AuxVariable is supplied to Sifgrs, gas release is not allowed unless
# that variable is > 0.5 locally. The PercolationUserObject checks whether each position is connected
# to a free surface and sets the AuxVariable accordingly.

# In this test, the gas released should be nearly the same as the sifgrs_second_stage test.

[Mesh]
  [mesh]
    type = FileMeshGenerator
    file = 1hex8_10mm_cube.e
  []
  [free1]
    type = SideSetsAroundSubdomainGenerator
    new_boundary = free1
    normal = '1 0 0'
    block = 1
    input = mesh
  []
[]

[Functions]
  [Temp_func]
    type = ParsedFunction
    expression = '1400'
  []
  [Fiss_func]
    type = ParsedFunction
    expression = '1.e19'
  []
[]

[Variables]
  [T]
    initial_condition = 1400
  []
[]

[AuxVariables]
  [fission_rate]
  []
  [GBCoverage]
    order = CONSTANT
    family = MONOMIAL
  []
  # percolation AuxVariables
  [open_coverage]
    order = CONSTANT
    family = MONOMIAL
  []
  [open_threshold]
    order = CONSTANT
    family = MONOMIAL
  []
  [open]
    order = CONSTANT
    family = MONOMIAL
  []
  [cluster]
    order = CONSTANT
    family = MONOMIAL
  []
  [percolated]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[Kernels]
  [heat]
    type = ADHeatConduction
    variable = T
  []
[]

[AuxKernels]
  [fissionrate]
    type = FissionRateGeneral
    fission_rate_formulation = GENERIC
    variable = fission_rate
    value = 1
    fission_rate_function = Fiss_func
    execute_on = 'initial timestep_begin'
  []
  [frcvrg]
    type = ADMaterialRealAux
    variable = GBCoverage
    property = GBCoverage
    execute_on = 'initial linear'
  []
  # percolation auxkernels
  [open_coverage]
    type = ADMaterialRealAux
    variable = open_coverage
    property = GBCoverage
  []
  [open_threshold]
    type = ADMaterialRealAux
    variable = open_threshold
    property = sat_coverage
  []
  [open]
    type = ParsedAux
    variable = open
    coupled_variables = 'open_coverage open_threshold'
    expression = 'open_coverage-open_threshold'
  []
  [cluster]
    type = FeatureFloodCountAux
    variable = cluster
    execute_on = 'timestep_begin'
    field_display = UNIQUE_REGION
    flood_counter = percolate
  []
  [percolated]
    type = PercolationAux
    variable = percolated
    execute_on = 'timestep_begin'
    percolation = percolate
  []
[]

[BCs]
  [bottom_T]
    type = ADFunctionDirichletBC
    variable = T
    function = Temp_func
    boundary = 1
  []
[]

[Materials]
  [UO2]
    type = ADHeatConductionMaterial
    block = 1
    thermal_conductivity = 1.0
    specific_heat = 1.0
  []
  [fission_gas_behavior]
    type = ADUO2Sifgrs
    block = 1
    temperature = T
    fission_rate = fission_rate
    percolation_to_surface = percolated
  []
[]

[Executioner]
  type = Transient
  solve_type = NEWTON

  l_tol = 1e-4
  nl_abs_tol = 1e-5
  nl_rel_tol = 1e-5
  start_time = 0.0
  num_steps = 50
  dt = 1e6
  end_time = 5e7
[]

[Postprocessors]
  [fis_gas_generated]
    type = ADElementIntegralFisGasGeneratedSifgrs
    block = 1
  []
  [fis_gas_released]
    type = ADElementIntegralFisGasReleasedSifgrs
    block = 1
  []
[]

[UserObjects]
  [percolate]
    type = PercolationUserObject
    execute_on = 'timestep_begin'
    boundaries = 'free1'
    variable = open
    threshold = 0.0
  []
[]

[Outputs]
  [out]
    type = Exodus
  []
[]

(test/tests/sifgrs/uo2/ad_percolation_xfem.i)

# This is to test gas release through elements that are cut by XFEM. A 2D domain is
# used and the LineSegmentCutUserObject is used to insert a crack from the right edge
# of the domain inward toward the left edge. Because of the boundary conditions on temperature,
# gas would not normally be released to the free surface on the left side, but
# with the crack present gas release occurs.

[GlobalParams]
  density = 10970.
  order = FIRST
  family = LAGRANGE
  energy_per_fission = 3.2e-11
[]

[Mesh]
  [mesh]
    type = GeneratedMeshGenerator
    dim = 2
    xmin = 0
    xmax = 0.005
    ymin = 0
    ymax = 0.005
    nx = 5
    ny = 5
  []
  [create_block2]
    type = RenameBlockGenerator
    input = mesh
    old_block = 0
    new_block = 2
  []
  [free1]
    type = SideSetsAroundSubdomainGenerator
    new_boundary = free1
    normal = '1 0 0'
    block = 2
    input = create_block2
  []
  [subdomain1]
    type = SubdomainBoundingBoxGenerator
    bottom_left = '0 0 0'
    top_right = '0.005 0.005 0'
    block_id = 2
    input = free1
  []
[]

#Create a notch in the mesh using XFEM
[XFEM]
  qrule = volfrac
  output_cut_plane = true
[]

[UserObjects]
  [line_seg_cut_uo]
    type = LineSegmentCutUserObject
    cut_data = '0.005 0.0025 0.001 0.0025'
    time_start_cut = 0.0
    time_end_cut = 0.0
  []
[]

[Variables]
  [temp]
    initial_condition = 673.
  []
[]

[AuxVariables]
  [grain_radius]
    block = 2
    initial_condition = 5.e-06
  []
  [gas_gen_3]
    order = CONSTANT
    family = MONOMIAL
    block = 2
  []
  [GBCoverage]
    order = CONSTANT
    family = MONOMIAL
  []
  [thermal_conductivity]
    order = CONSTANT
    family = MONOMIAL
    block = 2
  []
  [burnup]
    block = 2
  []
  [fission_rate]
    block = 2
  []

  # percolation variables
  [open_coverage]
    order = CONSTANT
    family = MONOMIAL
  []
  [open_threshold]
    order = CONSTANT
    family = MONOMIAL
  []
  [open]
    order = CONSTANT
    family = MONOMIAL
  []
  [cluster]
    order = CONSTANT
    family = MONOMIAL
  []
  [percolated]
    order = CONSTANT
    family = MONOMIAL
  []
[]

# Define functions to control power and boundary conditions
[Functions]
  [power_history]
    type = PiecewiseLinear
    x = '0.   10800.  1.0e+8'
    y = '0.   25.     25.   '
    scale_factor = 1000.
  []
  [pressure_ramp]
    type = PiecewiseLinear
    x = '0.     1.0e+8'
    y = '25.     25.'
    scale_factor = 1.0e+6
  []
[]

[Kernels]
  [heat] # gradient term in heat conduction equation
    type = ADHeatConduction
    variable = temp
  []
  [heat_ie] # time term in heat conduction equation
    type = ADHeatConductionTimeDerivative
    variable = temp
  []
  [heat_source] # source term in heat conduction equation
    type = ADNeutronHeatSource
    variable = temp
    block = 2
    fission_rate = fission_rate # coupling to the fission_rate aux variable
  []
[]

# Define auxilliary kernels for each of the aux variables
[AuxKernels]
  [fggen]
    type = ADMaterialRealAux
    variable = gas_gen_3
    property = gas_concentration_generated_total
  []
  [fractcov]
    type = ADMaterialRealAux
    variable = GBCoverage
    property = GBCoverage
    block = 2
  []
  [fuel_conductivity]
    type = ADMaterialRealAux
    variable = thermal_conductivity
    property = thermal_conductivity
  []
  [brnp]
    type = BurnupAux
    variable = burnup
    block = 2
    fission_rate = fission_rate
    molecular_weight = 0.270
  []
  [frate]
    type = FissionRateGeneral
    fission_rate_formulation = GENERIC
    variable = fission_rate
    block = 2
    value = 5.e+14
    fission_rate_function = power_history
  []

  # percolation auxkernels
  [open_coverage]
    type = ADMaterialRealAux
    variable = open_coverage
    property = GBCoverage
  []
  [open_threshold]
    type = ADMaterialRealAux
    variable = open_threshold
    property = 0.3 #GB coverage at which trijunction network is percolated
  []
  [open]
    type = ParsedAux
    variable = open
    coupled_variables = 'open_coverage open_threshold'
    expression = 'open_coverage-open_threshold'
  []
  [cluster]
    type = FeatureFloodCountAux
    variable = cluster
    execute_on = 'timestep_begin'
    field_display = UNIQUE_REGION
    flood_counter = percolate
  []
  [percolated]
    type = PercolationAux
    variable = percolated
    execute_on = 'timestep_begin'
    percolation = percolate
  []
[]

# Define boundary conditions
[BCs]
  [imposed_ext_temp]
    type = DirichletBC
    boundary = right
    variable = temp
    value = 673.
  []

  # insulate the top and bottom of this pellet
  [top_pellet]
    variable = temp
    value = 0.
    type = NeumannBC
    boundary = top
  []
  [bottom_pellet]
    variable = temp
    value = 0.
    type = NeumannBC
    boundary = bottom
  []
  [left_pellet]
    variable = temp
    value = 0.
    type = NeumannBC
    boundary = left
  []
[]

# Define material behavior models and input material property data
[Materials]
  [fuel_thermal]
    type = ADHeatConductionMaterial
    block = 2
    thermal_conductivity = 3.
    specific_heat = 400.
  []
  [fuel_density]
    type = ADParsedMaterial
    block = 2
    property_name = density
    expression = 10970
  []
  [fission_gas_release_and_swelling]
    type = ADUO2Sifgrs
    block = 2
    diff_coeff_option = TURNBULL_D1_D2
    transient_option = MICROCRACKING
    res_param_option = HETEROGENEOUS_WHITE
    temperature = temp
    fission_rate = fission_rate
    burnup = burnup
    initial_porosity = 0.
    percolation_to_surface = percolated
  []
[]

[Dampers]
  [limitT]
    type = MaxIncrement
    max_increment = 50.
    variable = temp
  []
[]

[Executioner]
  type = Transient
  solve_type = NEWTON

  petsc_options = '-ksp_gmres_modifiedgramschmidt'
  petsc_options_iname = '-ksp_gmres_restart -pc_type  -pc_composite_pcs -sub_0_pc_hypre_type -sub_0_pc_hypre_boomeramg_max_iter -sub_0_pc_hypre_boomeramg_grid_sweeps_all -sub_1_sub_pc_type -pc_composite_type -ksp_type -mat_mffd_type'
  petsc_options_value = '201                 composite hypre,asm         boomeramg            2                                  2                                         lu                 multiplicative     fgmres    ds'

  line_search = 'none'

  # controls for linear iterations
  l_max_its = 100
  l_tol = 1.0e-06

  # controls for nonlinear iterations
  nl_max_its = 10
  nl_rel_tol = 1.0e-4
  nl_abs_tol = 1.0e-8

  # time control
  start_time = 0.

  end_time = 1.0e+8
  num_steps = 5000
  dtmax = 1.0e+06
  dtmin = 1.0

  [TimeStepper]
    type = IterationAdaptiveDT
    dt = 1.0
    timestep_limiting_function = power_history
    max_function_change = 3000.
    force_step_every_function_point = true
  []
  [Quadrature]
    order = THIRD
  []
[]

[UserObjects]
  [percolate]
    type = PercolationUserObject
    execute_on = 'timestep_begin'
    boundaries = 'free1'
    variable = open
    threshold = 0.0
    use_xfem = true
  []
[]

# Define postprocessors (some are required as specified above; others are optional; many others are available)
[Postprocessors]
  [ave_burnup_EAV]
    type = ElementAverageValue
    block = 2
    variable = burnup
  []
  [fis_gas_released]
    type = ADElementIntegralFisGasReleasedSifgrs
    block = 2
  []
[]

# Define output file(s)
[Outputs]
  time_step_interval =  1
  csv = true
  exodus = true
  color = true
  print_linear_residuals = true
  [console]
    type = Console
    max_rows = 25
    output_linear = true
  []
[]

Input Parameters
Input Files