UPuZr Lanthanide Wastage

Calculates wastage thickness due to reactions between lanthanides and stainless steel cladding materials.

Description

The UPuZrLanthanideWastage class is used to calculate the wastage thickness due to reactions between lanthanides and stainless steel cladding materials. It is part of a mechanistic fuel-cladding chemical interaction (FCCI) modeling framework. See UPuZrLanthanideDiffusivity and UPuZrLanthanideFlux for more information.

The wastage layer velocity $var element = document.getElementById("moose-equation-5ce4d123-2394-4600-a781-16e33489d763");katex.render("v", element, {displayMode:false,throwOnError:false});$ is taken from Hirschhorn et al. (2025) and is given by: $(1)var element = document.getElementById("moose-equation-51c93fdc-ff58-4bca-8ac8-fa1a9e4f88f2");katex.render(" v = f_S V_m f_G f_{TV} J, ", element, {displayMode:true,throwOnError:false});$

where $var element = document.getElementById("moose-equation-ebc30b3f-0dcc-4777-9352-aed82a78e583");katex.render("f_S", element, {displayMode:false,throwOnError:false});$ is the stoichiometry factor, $var element = document.getElementById("moose-equation-e919827a-0c2b-46ee-aaeb-076299611343");katex.render("V_m", element, {displayMode:false,throwOnError:false});$ is the molar volume of the unreacted cladding, $var element = document.getElementById("moose-equation-41a2e961-516a-4b05-a793-77f32c59ee93");katex.render("f_G", element, {displayMode:false,throwOnError:false});$ is the geometry factor, $var element = document.getElementById("moose-equation-f4245b53-5c89-4587-94b4-5a47e5bd056b");katex.render("f_{TV}", element, {displayMode:false,throwOnError:false});$ is the thickness variability factor, and $var element = document.getElementById("moose-equation-e5093496-4cd5-4fff-a1f6-0245c12b6634");katex.render("J", element, {displayMode:false,throwOnError:false});$ is the lanthanide flux normal to the fuel surface. The model was derived for and is intended to be applied in 2D axisymmetric simulations only. The stoichiometry factor is derived by assuming that the wastage layer is composed of an intermetallic phase with the form (Fe,Cr,Ni) $var element = document.getElementById("moose-equation-8b0406ee-8ebd-4756-98e9-679a0918d97d");katex.render("_{17}", element, {displayMode:false,throwOnError:false});$ Ln $var element = document.getElementById("moose-equation-c2778624-c457-443c-be3d-368ed32c3c8d");katex.render("_2", element, {displayMode:false,throwOnError:false});$ , where Ln denotes lanthanides.

The geometry factor is applied to account for the reduction in lanthanide flux between the outer surface of the fuel and the outer surface of the wastage layer on the undeformed mesh. It is given by: $(2)var element = document.getElementById("moose-equation-8d074ceb-cec6-4c91-9b48-c5e8a0884227");katex.render(" f_G = \\frac{R_f}{R_f + t_g + \\delta}, ", element, {displayMode:true,throwOnError:false});$

where $var element = document.getElementById("moose-equation-fbef24f6-500b-4ff0-85e9-b556a9fab36d");katex.render("R_f", element, {displayMode:false,throwOnError:false});$ is the initial radius of the fuel, $var element = document.getElementById("moose-equation-a68559b6-2cda-4a66-a259-55d7a4f78068");katex.render("t_g", element, {displayMode:false,throwOnError:false});$ is the initial gap thickness, and $var element = document.getElementById("moose-equation-4a6cf7ad-f03d-46d4-8f0b-6bbda9f333c1");katex.render("\\delta", element, {displayMode:false,throwOnError:false});$ is the wastage layer thickness.

The thickness variability factor is applied to account for azimuthal variations in the thickness of the wastage layer at a given height in a fuel rod. It is given by: $(3)var element = document.getElementById("moose-equation-100db7ed-4c8d-4159-89e5-16b8e32e5df5");katex.render(" f_{TV} = \\frac{\\delta_{max}}{\\delta_{uniform}}, ", element, {displayMode:true,throwOnError:false});$

where $var element = document.getElementById("moose-equation-37dbfe25-1a78-4d7a-9470-5530638b0f1c");katex.render("\\delta_{max}", element, {displayMode:false,throwOnError:false});$ is the maximum wastage layer thickness observed at a given fuel rod height, and $var element = document.getElementById("moose-equation-854f9534-211b-4d17-9614-910d09374a71");katex.render("\\delta_{uniform}", element, {displayMode:false,throwOnError:false});$ is the thickness of an azimuthally uniform wastage layer that could form at that height.

Finally, wastage accumulates incrementally with each time step $var element = document.getElementById("moose-equation-987d8980-51f0-4b8d-860b-ca91f8ccc8e2");katex.render("i", element, {displayMode:false,throwOnError:false});$ , spanned by $var element = document.getElementById("moose-equation-911a7d52-585f-4a80-87a8-920a115f8c20");katex.render("\\Delta t_i", element, {displayMode:false,throwOnError:false});$ according to: $(4)var element = document.getElementById("moose-equation-437be0f6-0535-480a-bfcd-425c13f49f84");katex.render(" \\delta = \\sum_{i=1}^I \\delta_{i - 1} + v_i \\Delta t_i. ", element, {displayMode:true,throwOnError:false});$

See Hirschhorn et al. (2025) for more information.

FCCI Modeling Example

An example of the full mechanistic FCCI modeling framework is provided below. Lanthanide conservation, including production due to fission, transport through the fuel, and optional radioactive decay is described by: $(5)var element = document.getElementById("moose-equation-c8c52d6d-1293-4e10-87be-78d7cb7e6a45");katex.render(" \\frac{\\partial c}{\\partial t} = \\nabla \\cdot D \\nabla c + \\dot{F} \\gamma - \\lambda c, ", element, {displayMode:true,throwOnError:false});$

where $var element = document.getElementById("moose-equation-e081111c-7470-4a79-a148-9efe5bb97d7a");katex.render("\\dot{F}", element, {displayMode:false,throwOnError:false});$ is the fission rate density, $var element = document.getElementById("moose-equation-93966590-98d5-4ef8-b226-4ebf09cf8ff7");katex.render("\\gamma", element, {displayMode:false,throwOnError:false});$ is the effective lanthanide fission yield, and $var element = document.getElementById("moose-equation-f8bc19cd-5522-4408-8cd5-70e4f2fe78b9");katex.render("\\lambda", element, {displayMode:false,throwOnError:false});$ is the effective lanthanide decay constant. These physics can be modeled using existing BISON classes:

[Kernels<<<{"href": "../../syntax/Kernels/index.html"}>>>]
  [c_dt]
    type = TimeDerivative<<<{"description": "The time derivative operator with the weak form of $(\\psi_i, \\frac{\\partial u_h}{\\partial t})$.", "href": "../kernels/TimeDerivative.html"}>>>
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = c
  []
[]

[Kernels<<<{"href": "../../syntax/Kernels/index.html"}>>>]
  [c_source]
    type = NeutronHeatSource<<<{"description": "Compute heat generation due to fission.", "href": "../kernels/NeutronHeatSource.html"}>>>
    block<<<{"description": "The list of blocks (ids or names) that this object will be applied"}>>> = ${fuel_block_name}
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = c
    fission_rate<<<{"description": "Coupled Fission Rate"}>>> = fission_rate # fission/m^3-s
    energy_per_fission<<<{"description": "Energy Released per Fission"}>>> = ${production_constant} # mol/fission giving mol/m^3-s
  []
[]

[Kernels<<<{"href": "../../syntax/Kernels/index.html"}>>>]
  [c_diffusion]
    type = MatDiffusion<<<{"description": "Diffusion equation Kernel that takes an isotropic Diffusivity from a material property", "href": "../kernels/MatDiffusion.html"}>>>
    block<<<{"description": "The list of blocks (ids or names) that this object will be applied"}>>> = ${fuel_block_name}
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = c
    diffusivity<<<{"description": "The diffusivity value or material property"}>>> = D
    args<<<{"description": "Optional vector of arguments for the diffusivity. If provided and diffusivity is a derivative parsed material, Jacobian contributions from the diffusivity will be automatically computed"}>>> = 'c T'
  []
[]

[Kernels<<<{"href": "../../syntax/Kernels/index.html"}>>>]
  [c_decay]
    type = Decay<<<{"description": "Computes changing concentration due to radioactive decay.", "href": "../kernels/Decay.html"}>>>
    block<<<{"description": "The list of blocks (ids or names) that this object will be applied"}>>> = ${fuel_block_name}
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = c
    radioactive_decay_constant<<<{"description": "Radioactive decay constant"}>>> = ${decay_constant} # 1/s
  []
[]

The lanthanide diffusivity in the fuel is modeled using UPuZrLanthanideDiffusivity:

[Materials<<<{"href": "../../syntax/Materials/index.html"}>>>]
  [diffusivity]
    # informed by lower length scale simulations
    type = UPuZrLanthanideDiffusivity<<<{"description": "Calculates lanthanide diffusivity in U-Zr and U-Pu-Zr fuel.", "href": "UPuZrLanthanideDiffusivity.html"}>>>
    block<<<{"description": "The list of blocks (ids or names) that this object will be applied"}>>> = ${fuel_block_name}
    property_name<<<{"description": "Name of the parsed material property"}>>> = D
    temperature<<<{"description": "The temperature"}>>> = T
    porosity_name<<<{"description": "Name of the material property storing the porosity"}>>> = porosity
    sodium_logged_porosity_name<<<{"description": "Name of the material property storing the sodium-logged porosity"}>>> = sodium_logged_porosity
    outputs<<<{"description": "Vector of output names where you would like to restrict the output of variables(s) associated with this object"}>>> = exodus
    output_properties<<<{"description": "List of material properties, from this material, to output (outputs must also be defined to an output type)"}>>> = D
  []
[]

The lanthanide flux from the surface of the fuel into the cladding is modeled using UPuZrLanthanideFlux:

[Materials<<<{"href": "../../syntax/Materials/index.html"}>>>]
  [flux]
    # informed by lower length scale simulations
    type = UPuZrLanthanideFlux<<<{"description": "Calculates the flux of lanthanides from the surface of U-Zr/U-Pu-Zr fuels into stainless steel cladding materials.", "href": "UPuZrLanthanideFlux.html"}>>>
    boundary<<<{"description": "The list of boundaries (ids or names) from the mesh where this object applies"}>>> = ${fuel_surface_name}
    property_name<<<{"description": "Name of the parsed material property"}>>> = F
    temperature<<<{"description": "The temperature of the fuel"}>>> = T
    concentration<<<{"description": "The lanthanide concentration in the fuel"}>>> = c
    outputs<<<{"description": "Vector of output names where you would like to restrict the output of variables(s) associated with this object"}>>> = exodus
    output_properties<<<{"description": "List of material properties, from this material, to output (outputs must also be defined to an output type)"}>>> = F
  []
[]

The calculated flux is used to create a sink term to consume reacted lanthanides via a boundary condition imposed on the surface of the fuel using MatNeumannBC:

[BCs<<<{"href": "../../syntax/NuclearMaterials/BCs/index.html"}>>>]
  [c_right]
    type = MatNeumannBC<<<{"description": "Imposes the integrated boundary condition $\\frac{C \\partial u}{\\partial n}=M*h$, where $h$ is a constant, $M$ is a material property, and $C$ is a coefficient defined by the kernel for $u$.", "href": "../bcs/MatNeumannBC.html"}>>>
    boundary<<<{"description": "The list of boundary IDs from the mesh where this object applies"}>>> = ${fuel_surface_name}
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = c
    boundary_material<<<{"description": "Material property multiplying the constant that will be enforced by the BC"}>>> = F
    value<<<{"description": "For a Laplacian problem, the value of the gradient dotted with the normals on the boundary."}>>> = -1
  []
[]

Finally, UPuZrLanthanideWastage is used to calculate the wastage thickness due lanthanides removed by the boundary condition:

[Materials<<<{"href": "../../syntax/Materials/index.html"}>>>]
  [wastage_thickness]
    # informed by lower length scale simulations
    type = UPuZrLanthanideWastage<<<{"description": "Calculates wastage thickness due to reactions between lanthanides and stainless steel cladding materials.", "href": "UPuZrLanthanideWastage.html"}>>>
    boundary<<<{"description": "The list of boundaries (ids or names) from the mesh where this object applies"}>>> = ${fuel_surface_name}
    cladding_density<<<{"description": "The initial density of the cladding in kg/m^3"}>>> = ${cladding_density}
    fuel_outer_radius<<<{"description": "The initial outer fuel radius in meters"}>>> = ${fuel_outer_radius}
    gap_thickness<<<{"description": "The initial gap thickness in meters"}>>> = ${gap_thickness}
    lanthanide_flux<<<{"description": "The lanthanide flux in mol/m^2-s"}>>> = F
    outputs<<<{"description": "Vector of output names where you would like to restrict the output of variables(s) associated with this object"}>>> = exodus
  []
[]

The calculated wastage thickness can be coupled into the cladding thermomechanics solve using methods previously developed for empirically calculated wastage thicknesses (e.g., see HT9ElasticityTensor, MetallicFuelWastageDamage, and associated classes). The example presented above is setup using MultiApp functionality for compatibility with a variety of different manually-developed and FIPD-powered metallic fuel assessment cases, but it can also be fully coupled with thermomechanics solves if desired. See Hirschhorn et al. (2025) for more information.

Example Input Syntax

[Materials<<<{"href": "../../syntax/Materials/index.html"}>>>]
  [wastage_thickness]
    type = UPuZrLanthanideWastage<<<{"description": "Calculates wastage thickness due to reactions between lanthanides and stainless steel cladding materials.", "href": "UPuZrLanthanideWastage.html"}>>>
    cladding_stoichiometry<<<{"description": "The stoichiometry of (iron,chromium,nickel) in the wastage layer"}>>> = ${cladding_stoichiometry}
    lanthanide_stoichiometry<<<{"description": "The stoichiometry of lanthanides in the wastage layer"}>>> = ${lanthanide_stoichiometry}
    cladding_molar_mass<<<{"description": "The molar mass of the cladding in kg/mol (defaults to that of pure iron)"}>>> = ${cladding_molar_mass}
    cladding_density<<<{"description": "The initial density of the cladding in kg/m^3"}>>> = ${cladding_density}
    fuel_outer_radius<<<{"description": "The initial outer fuel radius in meters"}>>> = ${fuel_outer_radius}
    gap_thickness<<<{"description": "The initial gap thickness in meters"}>>> = ${gap_thickness}
    thickness_variability_factor<<<{"description": "The ratio of maximum to uniform wastage thickness"}>>> = ${thickness_variability_factor}
    lanthanide_flux<<<{"description": "The lanthanide flux in mol/m^2-s"}>>> = lanthanide_flux
    outputs<<<{"description": "Vector of output names where you would like to restrict the output of variables(s) associated with this object"}>>> = exodus
  []
[]

Input Parameters

cladding_densityThe initial density of the cladding in kg/m^3
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:The initial density of the cladding in kg/m^3
fuel_outer_radiusThe initial outer fuel radius in meters
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:The initial outer fuel radius in meters
gap_thicknessThe initial gap thickness in meters
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:The initial gap thickness in meters

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
cladding_molar_mass0.0558The molar mass of the cladding in kg/mol (defaults to that of pure iron)
Default:0.0558
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:The molar mass of the cladding in kg/mol (defaults to that of pure iron)
cladding_stoichiometry17The stoichiometry of (iron,chromium,nickel) in the wastage layer
Default:17
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:The stoichiometry of (iron,chromium,nickel) in the wastage layer
computeTrueWhen false, MOOSE will not call compute methods on this material. The user must call computeProperties() after retrieving the MaterialBase via MaterialBasePropertyInterface::getMaterialBase(). Non-computed MaterialBases are not sorted for dependencies.
Default:True
C++ Type:bool
Controllable:No
Description:When false, MOOSE will not call compute methods on this material. The user must call computeProperties() after retrieving the MaterialBase via MaterialBasePropertyInterface::getMaterialBase(). Non-computed MaterialBases are not sorted for dependencies.
constant_onNONEWhen ELEMENT, MOOSE will only call computeQpProperties() for the 0th quadrature point, and then copy that value to the other qps.When SUBDOMAIN, MOOSE will only call computeQpProperties() for the 0th quadrature point, and then copy that value to the other qps. Evaluations on element qps will be skipped
Default:NONE
C++ Type:MooseEnum
Options:NONE, ELEMENT, SUBDOMAIN
Controllable:No
Description:When ELEMENT, MOOSE will only call computeQpProperties() for the 0th quadrature point, and then copy that value to the other qps.When SUBDOMAIN, MOOSE will only call computeQpProperties() for the 0th quadrature point, and then copy that value to the other qps. Evaluations on element qps will be skipped
declare_suffixAn optional suffix parameter that can be appended to any declared 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 declared properties. The suffix will be prepended with a '_' character.
lanthanide_fluxFThe lanthanide flux in mol/m^2-s
Default:F
C++ Type:MaterialPropertyName
Unit:(no unit assumed)
Controllable:No
Description:The lanthanide flux in mol/m^2-s
lanthanide_stoichiometry2The stoichiometry of lanthanides in the wastage layer
Default:2
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:The stoichiometry of lanthanides in the wastage layer
thickness_variability_factor2The ratio of maximum to uniform wastage thickness
Default:2
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:The ratio of maximum to uniform wastage thickness

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.
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
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

output_propertiesList of material properties, from this material, to output (outputs must also be defined to an output type)
C++ Type:std::vector<std::string>
Controllable:No
Description:List of material properties, from this material, to output (outputs must also be defined to an output type)
outputsnone Vector of output names where you would like to restrict the output of variables(s) associated with this object
Default:none
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

Outputs 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/metal_fuel/mechanistic_fcci/fcci.i)
(test/tests/upuzr_lanthanide_wastage/test.i)

References

J.A. Hirschhorn, L.K. Aagesen, C. Jiang, and G.L. Beausoleil. Development and preliminary validation of a mechanistic multiscale model for fuel-cladding chemical interaction in metallic nuclear fuels. Nuclear Engineering and Design, 432:113811, 2025. doi:10.1016/j.nucengdes.2024.113811.

@article{HIRSCHHORN2025113811,
    author = "Hirschhorn, J.A. and Aagesen, L.K. and Jiang, C. and Beausoleil, G.L.",
    title = "Development and preliminary validation of a mechanistic multiscale model for fuel-cladding chemical interaction in metallic nuclear fuels",
    journal = "Nuclear Engineering and Design",
    volume = "432",
    pages = "113811",
    year = "2025",
    issn = "0029-5493",
    doi = "10.1016/j.nucengdes.2024.113811"
}

(examples/metal_fuel/mechanistic_fcci/fcci.i)

# This example exercises the mechanistic Fuel-Cladding Chemical Interaction
# (FCCI) modeling approach for U-Zr and U-Pu-Zr metallic nuclear fuels. It is
# run as a SubApp, which is called by the combination of an existing assessment
# case and XXXX_multiapp.i.

# It is a collection of BISON classes and objects needed to apply a mechanistic
# FCCI model for U-Zr and U-Pu-Zr metallic nuclear fuels. It is designed to
# complement the modeling approaches adopted by the FIPD-powered X447 assessment
# cases and manually-developed X430 and IFR1 assessment cases. Thermomechanical
# behaviors are modeled in the existing assessment cases whereas lanthanide (Ln)
# transport, FCCI, and wastage growth are modeled in the SubApp. XXXX_multiapp.i
# then overrides the empirical FCCI model currently used in the assessments and
# replaces it with the mechanistic FCCI model. Examples of how to do this are
# included in the test and example specifications.

# Note that, in this model, c indicates the stable concentration of Lns. The
# model relies on an effective diffusion coefficient and flux terms informed by
# lower length scale modeling and simulations. Decay terms are included for
# illustration purposes but do not affect the solution.

# combined effective Ln production constant in mol/fission
ln_yield = 0.3 # atom/fission
avogadro = 6.0221e23 # atom/mol
production_constant = '${fparse ln_yield / avogadro}' # mol/fission

# combined effective Ln decay constant in 1/s
decay_constant = 0

# variable order, block and boundary names, and end time used in the assessment
order = placeholder
fuel_block_name = placeholder
fuel_surface_name = placeholder
end_time = placeholder

# fuel rod geometry and material properties used in the assessment
cladding_density = placeholder
fuel_outer_radius = placeholder
gap_thickness = placeholder

[GlobalParams]
  order = ${order}
  family = LAGRANGE
[]

[Problem]
  # nothing is being solved for on the cladding
  kernel_coverage_check = false
  material_coverage_check = false
[]

[Mesh]
[]

[Variables]
  [c] # stable Ln concentration in mol/m^3
    block = ${fuel_block_name}
  []
[]

[AuxVariables]
  [T]
    initial_condition = 298
  []
  [fission_rate]
    block = ${fuel_block_name}
    family = MONOMIAL
    order = CONSTANT
  []
  [porosity_aux]
    block = ${fuel_block_name}
    family = MONOMIAL
    order = CONSTANT
  []
  [sodium_logged_porosity_aux]
    block = ${fuel_block_name}
    family = MONOMIAL
    order = CONSTANT
  []
  [diffusivity]
    block = ${fuel_block_name}
    family = MONOMIAL
    order = CONSTANT
  []
  [dcdx]
    block = ${fuel_block_name}
    family = MONOMIAL
    order = CONSTANT
  []
  [c_flux]
    block = ${fuel_block_name}
    family = MONOMIAL
    order = CONSTANT
  []
[]

[AuxKernels]
  [diffusivity]
    type = MaterialRealAux
    boundary = ${fuel_surface_name}
    variable = diffusivity
    property = D
  []
  [dcdx]
    type = VariableGradientComponent
    boundary = ${fuel_surface_name}
    variable = dcdx
    gradient_variable = c
    component = x
  []
  [c_flux]
    type = ParsedAux
    boundary = ${fuel_surface_name}
    variable = c_flux
    coupled_variables = 'diffusivity dcdx'
    expression = '-diffusivity * dcdx'
  []
[]

[Kernels]
  [c_dt]
    type = TimeDerivative
    variable = c
  []
  [c_diffusion]
    type = MatDiffusion
    block = ${fuel_block_name}
    variable = c
    diffusivity = D
    args = 'c T'
  []
  [c_source]
    type = NeutronHeatSource
    block = ${fuel_block_name}
    variable = c
    fission_rate = fission_rate # fission/m^3-s
    energy_per_fission = ${production_constant} # mol/fission giving mol/m^3-s
  []
  [c_decay]
    type = Decay
    block = ${fuel_block_name}
    variable = c
    radioactive_decay_constant = ${decay_constant} # 1/s
  []
[]

[Materials]
  [porosity]
    type = ParsedMaterial
    block = ${fuel_block_name}
    property_name = porosity
    coupled_variables = porosity_aux
    expression = porosity_aux
  []
  [sodium_logged_porosity]
    type = ParsedMaterial
    block = ${fuel_block_name}
    property_name = sodium_logged_porosity
    coupled_variables = sodium_logged_porosity_aux
    expression = sodium_logged_porosity_aux
  []
  [diffusivity]
    # informed by lower length scale simulations
    type = UPuZrLanthanideDiffusivity
    block = ${fuel_block_name}
    property_name = D
    temperature = T
    porosity_name = porosity
    sodium_logged_porosity_name = sodium_logged_porosity
    outputs = exodus
    output_properties = D
  []
  [flux]
    # informed by lower length scale simulations
    type = UPuZrLanthanideFlux
    boundary = ${fuel_surface_name}
    property_name = F
    temperature = T
    concentration = c
    outputs = exodus
    output_properties = F
  []
  [wastage_thickness]
    # informed by lower length scale simulations
    type = UPuZrLanthanideWastage
    boundary = ${fuel_surface_name}
    cladding_density = ${cladding_density}
    fuel_outer_radius = ${fuel_outer_radius}
    gap_thickness =${gap_thickness}
    lanthanide_flux = F
    outputs = exodus
  []
[]

[BCs]
  [c_right]
    type = MatNeumannBC
    boundary = ${fuel_surface_name}
    variable = c
    boundary_material = F
    value = -1
  []
[]

[Executioner]
  type = Transient
  solve_type = PJFNK
  automatic_scaling = true
  compute_scaling_once = false
  petsc_options_iname = '-pc_type -pc_factor_mat_solver_package -pc_factor_shift_type -pc_factor_shift_amount'
  petsc_options_value = 'lu       superlu_dist                  NONZERO               1e-15'
  line_search = NONE
  l_max_its = 30
  l_tol = 1e-3
  nl_max_its = 30
  nl_rel_tol = 1e-10
  nl_abs_tol = 1e-6
  start_time = 0
  dt = 1e7
  end_time = ${end_time}
  verbose = true
[]

[Postprocessors]
  [c_in_fuel] # mol
    type = ElementIntegralVariablePostprocessor
    block = ${fuel_block_name}
    variable = c
    execute_on = 'initial timestep_end'
    outputs = 'console csv'
  []
  [fission_rate_total] # fission/s
    type = ElementIntegralVariablePostprocessor
    block = ${fuel_block_name}
    variable = fission_rate
    execute_on = 'initial timestep_end'
    outputs = csv
  []
  [fission_total] # fission
    type = TimeIntegratedPostprocessor
    value = fission_rate_total
    execute_on = 'initial timestep_end'
    outputs = csv
  []
  [c_produced] # mol
    type = LinearCombinationPostprocessor
    pp_names = fission_total
    pp_coefs = ${production_constant} # mol/fission giving mol
    execute_on = 'initial timestep_end'
    outputs = 'console csv'
  []
  [c_decay_rate] # mol/s
    type = LinearCombinationPostprocessor
    pp_names = c_in_fuel # mol
    pp_coefs = ${decay_constant} # 1/s
    execute_on = 'initial timestep_end'
    outputs = csv
  []
  [c_decayed] # mol
    type = TimeIntegratedPostprocessor
    value = c_decay_rate
    execute_on = 'initial timestep_end'
    outputs = csv
  []
  [c_reaction_rate] # mol/s
    type = SideDiffusiveFluxIntegral
    boundary = ${fuel_surface_name}
    variable = c
    diffusivity = D
    execute_on = 'initial timestep_end'
    outputs = csv
  []
  [c_reacted] # mol
    type = TimeIntegratedPostprocessor
    value = c_reaction_rate
    execute_on = 'initial timestep_end'
    outputs = 'console csv'
  []
  [c_flux_max]
    type = SideExtremeValue
    boundary = ${fuel_surface_name}
    variable = c_flux
    value_type = max
    execute_on = 'initial timestep_end'
    outputs = csv
  []
  [c_flux_min]
    type = SideExtremeValue
    boundary = ${fuel_surface_name}
    variable = c_flux
    value_type = min
    execute_on = 'initial timestep_end'
    outputs = csv
  []
  [wastage_thickness_max] # m
    type = ElementExtremeValue
    variable = wastage_thickness
    value_type = max
    execute_on = 'initial timestep_end'
    outputs = 'console csv'
  []
  [c_surface_max] # mol
    type = SideExtremeValue
    boundary = ${fuel_surface_name}
    variable = c
    value_type = max
    execute_on = 'initial timestep_end'
    outputs = csv
  []
  [c_surface_min] # mol
    type = SideExtremeValue
    boundary = ${fuel_surface_name}
    variable = c
    value_type = min
    execute_on = 'initial timestep_end'
    outputs = csv
  []
[]

# [VectorPostprocessors]
#   [surface_conditions]
#     type = SideValueSampler
#     variable = 'T D F c c_flux wastage_thickness'
#     boundary = ${fuel_surface_name}
#     sort_by = y
#     execute_on = 'initial timestep_end'
#     outputs = csv
#   []
# []

[Outputs]
  csv = true
  exodus = true
[]

(examples/metal_fuel/mechanistic_fcci/fcci.i)

# This example exercises the mechanistic Fuel-Cladding Chemical Interaction
# (FCCI) modeling approach for U-Zr and U-Pu-Zr metallic nuclear fuels. It is
# run as a SubApp, which is called by the combination of an existing assessment
# case and XXXX_multiapp.i.

# It is a collection of BISON classes and objects needed to apply a mechanistic
# FCCI model for U-Zr and U-Pu-Zr metallic nuclear fuels. It is designed to
# complement the modeling approaches adopted by the FIPD-powered X447 assessment
# cases and manually-developed X430 and IFR1 assessment cases. Thermomechanical
# behaviors are modeled in the existing assessment cases whereas lanthanide (Ln)
# transport, FCCI, and wastage growth are modeled in the SubApp. XXXX_multiapp.i
# then overrides the empirical FCCI model currently used in the assessments and
# replaces it with the mechanistic FCCI model. Examples of how to do this are
# included in the test and example specifications.

# Note that, in this model, c indicates the stable concentration of Lns. The
# model relies on an effective diffusion coefficient and flux terms informed by
# lower length scale modeling and simulations. Decay terms are included for
# illustration purposes but do not affect the solution.

# combined effective Ln production constant in mol/fission
ln_yield = 0.3 # atom/fission
avogadro = 6.0221e23 # atom/mol
production_constant = '${fparse ln_yield / avogadro}' # mol/fission

# combined effective Ln decay constant in 1/s
decay_constant = 0

# variable order, block and boundary names, and end time used in the assessment
order = placeholder
fuel_block_name = placeholder
fuel_surface_name = placeholder
end_time = placeholder

# fuel rod geometry and material properties used in the assessment
cladding_density = placeholder
fuel_outer_radius = placeholder
gap_thickness = placeholder

[GlobalParams]
  order = ${order}
  family = LAGRANGE
[]

[Problem]
  # nothing is being solved for on the cladding
  kernel_coverage_check = false
  material_coverage_check = false
[]

[Mesh]
[]

[Variables]
  [c] # stable Ln concentration in mol/m^3
    block = ${fuel_block_name}
  []
[]

[AuxVariables]
  [T]
    initial_condition = 298
  []
  [fission_rate]
    block = ${fuel_block_name}
    family = MONOMIAL
    order = CONSTANT
  []
  [porosity_aux]
    block = ${fuel_block_name}
    family = MONOMIAL
    order = CONSTANT
  []
  [sodium_logged_porosity_aux]
    block = ${fuel_block_name}
    family = MONOMIAL
    order = CONSTANT
  []
  [diffusivity]
    block = ${fuel_block_name}
    family = MONOMIAL
    order = CONSTANT
  []
  [dcdx]
    block = ${fuel_block_name}
    family = MONOMIAL
    order = CONSTANT
  []
  [c_flux]
    block = ${fuel_block_name}
    family = MONOMIAL
    order = CONSTANT
  []
[]

[AuxKernels]
  [diffusivity]
    type = MaterialRealAux
    boundary = ${fuel_surface_name}
    variable = diffusivity
    property = D
  []
  [dcdx]
    type = VariableGradientComponent
    boundary = ${fuel_surface_name}
    variable = dcdx
    gradient_variable = c
    component = x
  []
  [c_flux]
    type = ParsedAux
    boundary = ${fuel_surface_name}
    variable = c_flux
    coupled_variables = 'diffusivity dcdx'
    expression = '-diffusivity * dcdx'
  []
[]

[Kernels]
  [c_dt]
    type = TimeDerivative
    variable = c
  []
  [c_diffusion]
    type = MatDiffusion
    block = ${fuel_block_name}
    variable = c
    diffusivity = D
    args = 'c T'
  []
  [c_source]
    type = NeutronHeatSource
    block = ${fuel_block_name}
    variable = c
    fission_rate = fission_rate # fission/m^3-s
    energy_per_fission = ${production_constant} # mol/fission giving mol/m^3-s
  []
  [c_decay]
    type = Decay
    block = ${fuel_block_name}
    variable = c
    radioactive_decay_constant = ${decay_constant} # 1/s
  []
[]

[Materials]
  [porosity]
    type = ParsedMaterial
    block = ${fuel_block_name}
    property_name = porosity
    coupled_variables = porosity_aux
    expression = porosity_aux
  []
  [sodium_logged_porosity]
    type = ParsedMaterial
    block = ${fuel_block_name}
    property_name = sodium_logged_porosity
    coupled_variables = sodium_logged_porosity_aux
    expression = sodium_logged_porosity_aux
  []
  [diffusivity]
    # informed by lower length scale simulations
    type = UPuZrLanthanideDiffusivity
    block = ${fuel_block_name}
    property_name = D
    temperature = T
    porosity_name = porosity
    sodium_logged_porosity_name = sodium_logged_porosity
    outputs = exodus
    output_properties = D
  []
  [flux]
    # informed by lower length scale simulations
    type = UPuZrLanthanideFlux
    boundary = ${fuel_surface_name}
    property_name = F
    temperature = T
    concentration = c
    outputs = exodus
    output_properties = F
  []
  [wastage_thickness]
    # informed by lower length scale simulations
    type = UPuZrLanthanideWastage
    boundary = ${fuel_surface_name}
    cladding_density = ${cladding_density}
    fuel_outer_radius = ${fuel_outer_radius}
    gap_thickness =${gap_thickness}
    lanthanide_flux = F
    outputs = exodus
  []
[]

[BCs]
  [c_right]
    type = MatNeumannBC
    boundary = ${fuel_surface_name}
    variable = c
    boundary_material = F
    value = -1
  []
[]

[Executioner]
  type = Transient
  solve_type = PJFNK
  automatic_scaling = true
  compute_scaling_once = false
  petsc_options_iname = '-pc_type -pc_factor_mat_solver_package -pc_factor_shift_type -pc_factor_shift_amount'
  petsc_options_value = 'lu       superlu_dist                  NONZERO               1e-15'
  line_search = NONE
  l_max_its = 30
  l_tol = 1e-3
  nl_max_its = 30
  nl_rel_tol = 1e-10
  nl_abs_tol = 1e-6
  start_time = 0
  dt = 1e7
  end_time = ${end_time}
  verbose = true
[]

[Postprocessors]
  [c_in_fuel] # mol
    type = ElementIntegralVariablePostprocessor
    block = ${fuel_block_name}
    variable = c
    execute_on = 'initial timestep_end'
    outputs = 'console csv'
  []
  [fission_rate_total] # fission/s
    type = ElementIntegralVariablePostprocessor
    block = ${fuel_block_name}
    variable = fission_rate
    execute_on = 'initial timestep_end'
    outputs = csv
  []
  [fission_total] # fission
    type = TimeIntegratedPostprocessor
    value = fission_rate_total
    execute_on = 'initial timestep_end'
    outputs = csv
  []
  [c_produced] # mol
    type = LinearCombinationPostprocessor
    pp_names = fission_total
    pp_coefs = ${production_constant} # mol/fission giving mol
    execute_on = 'initial timestep_end'
    outputs = 'console csv'
  []
  [c_decay_rate] # mol/s
    type = LinearCombinationPostprocessor
    pp_names = c_in_fuel # mol
    pp_coefs = ${decay_constant} # 1/s
    execute_on = 'initial timestep_end'
    outputs = csv
  []
  [c_decayed] # mol
    type = TimeIntegratedPostprocessor
    value = c_decay_rate
    execute_on = 'initial timestep_end'
    outputs = csv
  []
  [c_reaction_rate] # mol/s
    type = SideDiffusiveFluxIntegral
    boundary = ${fuel_surface_name}
    variable = c
    diffusivity = D
    execute_on = 'initial timestep_end'
    outputs = csv
  []
  [c_reacted] # mol
    type = TimeIntegratedPostprocessor
    value = c_reaction_rate
    execute_on = 'initial timestep_end'
    outputs = 'console csv'
  []
  [c_flux_max]
    type = SideExtremeValue
    boundary = ${fuel_surface_name}
    variable = c_flux
    value_type = max
    execute_on = 'initial timestep_end'
    outputs = csv
  []
  [c_flux_min]
    type = SideExtremeValue
    boundary = ${fuel_surface_name}
    variable = c_flux
    value_type = min
    execute_on = 'initial timestep_end'
    outputs = csv
  []
  [wastage_thickness_max] # m
    type = ElementExtremeValue
    variable = wastage_thickness
    value_type = max
    execute_on = 'initial timestep_end'
    outputs = 'console csv'
  []
  [c_surface_max] # mol
    type = SideExtremeValue
    boundary = ${fuel_surface_name}
    variable = c
    value_type = max
    execute_on = 'initial timestep_end'
    outputs = csv
  []
  [c_surface_min] # mol
    type = SideExtremeValue
    boundary = ${fuel_surface_name}
    variable = c
    value_type = min
    execute_on = 'initial timestep_end'
    outputs = csv
  []
[]

# [VectorPostprocessors]
#   [surface_conditions]
#     type = SideValueSampler
#     variable = 'T D F c c_flux wastage_thickness'
#     boundary = ${fuel_surface_name}
#     sort_by = y
#     execute_on = 'initial timestep_end'
#     outputs = csv
#   []
# []

[Outputs]
  csv = true
  exodus = true
[]

(examples/metal_fuel/mechanistic_fcci/fcci.i)

# This example exercises the mechanistic Fuel-Cladding Chemical Interaction
# (FCCI) modeling approach for U-Zr and U-Pu-Zr metallic nuclear fuels. It is
# run as a SubApp, which is called by the combination of an existing assessment
# case and XXXX_multiapp.i.

# It is a collection of BISON classes and objects needed to apply a mechanistic
# FCCI model for U-Zr and U-Pu-Zr metallic nuclear fuels. It is designed to
# complement the modeling approaches adopted by the FIPD-powered X447 assessment
# cases and manually-developed X430 and IFR1 assessment cases. Thermomechanical
# behaviors are modeled in the existing assessment cases whereas lanthanide (Ln)
# transport, FCCI, and wastage growth are modeled in the SubApp. XXXX_multiapp.i
# then overrides the empirical FCCI model currently used in the assessments and
# replaces it with the mechanistic FCCI model. Examples of how to do this are
# included in the test and example specifications.

# Note that, in this model, c indicates the stable concentration of Lns. The
# model relies on an effective diffusion coefficient and flux terms informed by
# lower length scale modeling and simulations. Decay terms are included for
# illustration purposes but do not affect the solution.

# combined effective Ln production constant in mol/fission
ln_yield = 0.3 # atom/fission
avogadro = 6.0221e23 # atom/mol
production_constant = '${fparse ln_yield / avogadro}' # mol/fission

# combined effective Ln decay constant in 1/s
decay_constant = 0

# variable order, block and boundary names, and end time used in the assessment
order = placeholder
fuel_block_name = placeholder
fuel_surface_name = placeholder
end_time = placeholder

# fuel rod geometry and material properties used in the assessment
cladding_density = placeholder
fuel_outer_radius = placeholder
gap_thickness = placeholder

[GlobalParams]
  order = ${order}
  family = LAGRANGE
[]

[Problem]
  # nothing is being solved for on the cladding
  kernel_coverage_check = false
  material_coverage_check = false
[]

[Mesh]
[]

[Variables]
  [c] # stable Ln concentration in mol/m^3
    block = ${fuel_block_name}
  []
[]

[AuxVariables]
  [T]
    initial_condition = 298
  []
  [fission_rate]
    block = ${fuel_block_name}
    family = MONOMIAL
    order = CONSTANT
  []
  [porosity_aux]
    block = ${fuel_block_name}
    family = MONOMIAL
    order = CONSTANT
  []
  [sodium_logged_porosity_aux]
    block = ${fuel_block_name}
    family = MONOMIAL
    order = CONSTANT
  []
  [diffusivity]
    block = ${fuel_block_name}
    family = MONOMIAL
    order = CONSTANT
  []
  [dcdx]
    block = ${fuel_block_name}
    family = MONOMIAL
    order = CONSTANT
  []
  [c_flux]
    block = ${fuel_block_name}
    family = MONOMIAL
    order = CONSTANT
  []
[]

[AuxKernels]
  [diffusivity]
    type = MaterialRealAux
    boundary = ${fuel_surface_name}
    variable = diffusivity
    property = D
  []
  [dcdx]
    type = VariableGradientComponent
    boundary = ${fuel_surface_name}
    variable = dcdx
    gradient_variable = c
    component = x
  []
  [c_flux]
    type = ParsedAux
    boundary = ${fuel_surface_name}
    variable = c_flux
    coupled_variables = 'diffusivity dcdx'
    expression = '-diffusivity * dcdx'
  []
[]

[Kernels]
  [c_dt]
    type = TimeDerivative
    variable = c
  []
  [c_diffusion]
    type = MatDiffusion
    block = ${fuel_block_name}
    variable = c
    diffusivity = D
    args = 'c T'
  []
  [c_source]
    type = NeutronHeatSource
    block = ${fuel_block_name}
    variable = c
    fission_rate = fission_rate # fission/m^3-s
    energy_per_fission = ${production_constant} # mol/fission giving mol/m^3-s
  []
  [c_decay]
    type = Decay
    block = ${fuel_block_name}
    variable = c
    radioactive_decay_constant = ${decay_constant} # 1/s
  []
[]

[Materials]
  [porosity]
    type = ParsedMaterial
    block = ${fuel_block_name}
    property_name = porosity
    coupled_variables = porosity_aux
    expression = porosity_aux
  []
  [sodium_logged_porosity]
    type = ParsedMaterial
    block = ${fuel_block_name}
    property_name = sodium_logged_porosity
    coupled_variables = sodium_logged_porosity_aux
    expression = sodium_logged_porosity_aux
  []
  [diffusivity]
    # informed by lower length scale simulations
    type = UPuZrLanthanideDiffusivity
    block = ${fuel_block_name}
    property_name = D
    temperature = T
    porosity_name = porosity
    sodium_logged_porosity_name = sodium_logged_porosity
    outputs = exodus
    output_properties = D
  []
  [flux]
    # informed by lower length scale simulations
    type = UPuZrLanthanideFlux
    boundary = ${fuel_surface_name}
    property_name = F
    temperature = T
    concentration = c
    outputs = exodus
    output_properties = F
  []
  [wastage_thickness]
    # informed by lower length scale simulations
    type = UPuZrLanthanideWastage
    boundary = ${fuel_surface_name}
    cladding_density = ${cladding_density}
    fuel_outer_radius = ${fuel_outer_radius}
    gap_thickness =${gap_thickness}
    lanthanide_flux = F
    outputs = exodus
  []
[]

[BCs]
  [c_right]
    type = MatNeumannBC
    boundary = ${fuel_surface_name}
    variable = c
    boundary_material = F
    value = -1
  []
[]

[Executioner]
  type = Transient
  solve_type = PJFNK
  automatic_scaling = true
  compute_scaling_once = false
  petsc_options_iname = '-pc_type -pc_factor_mat_solver_package -pc_factor_shift_type -pc_factor_shift_amount'
  petsc_options_value = 'lu       superlu_dist                  NONZERO               1e-15'
  line_search = NONE
  l_max_its = 30
  l_tol = 1e-3
  nl_max_its = 30
  nl_rel_tol = 1e-10
  nl_abs_tol = 1e-6
  start_time = 0
  dt = 1e7
  end_time = ${end_time}
  verbose = true
[]

[Postprocessors]
  [c_in_fuel] # mol
    type = ElementIntegralVariablePostprocessor
    block = ${fuel_block_name}
    variable = c
    execute_on = 'initial timestep_end'
    outputs = 'console csv'
  []
  [fission_rate_total] # fission/s
    type = ElementIntegralVariablePostprocessor
    block = ${fuel_block_name}
    variable = fission_rate
    execute_on = 'initial timestep_end'
    outputs = csv
  []
  [fission_total] # fission
    type = TimeIntegratedPostprocessor
    value = fission_rate_total
    execute_on = 'initial timestep_end'
    outputs = csv
  []
  [c_produced] # mol
    type = LinearCombinationPostprocessor
    pp_names = fission_total
    pp_coefs = ${production_constant} # mol/fission giving mol
    execute_on = 'initial timestep_end'
    outputs = 'console csv'
  []
  [c_decay_rate] # mol/s
    type = LinearCombinationPostprocessor
    pp_names = c_in_fuel # mol
    pp_coefs = ${decay_constant} # 1/s
    execute_on = 'initial timestep_end'
    outputs = csv
  []
  [c_decayed] # mol
    type = TimeIntegratedPostprocessor
    value = c_decay_rate
    execute_on = 'initial timestep_end'
    outputs = csv
  []
  [c_reaction_rate] # mol/s
    type = SideDiffusiveFluxIntegral
    boundary = ${fuel_surface_name}
    variable = c
    diffusivity = D
    execute_on = 'initial timestep_end'
    outputs = csv
  []
  [c_reacted] # mol
    type = TimeIntegratedPostprocessor
    value = c_reaction_rate
    execute_on = 'initial timestep_end'
    outputs = 'console csv'
  []
  [c_flux_max]
    type = SideExtremeValue
    boundary = ${fuel_surface_name}
    variable = c_flux
    value_type = max
    execute_on = 'initial timestep_end'
    outputs = csv
  []
  [c_flux_min]
    type = SideExtremeValue
    boundary = ${fuel_surface_name}
    variable = c_flux
    value_type = min
    execute_on = 'initial timestep_end'
    outputs = csv
  []
  [wastage_thickness_max] # m
    type = ElementExtremeValue
    variable = wastage_thickness
    value_type = max
    execute_on = 'initial timestep_end'
    outputs = 'console csv'
  []
  [c_surface_max] # mol
    type = SideExtremeValue
    boundary = ${fuel_surface_name}
    variable = c
    value_type = max
    execute_on = 'initial timestep_end'
    outputs = csv
  []
  [c_surface_min] # mol
    type = SideExtremeValue
    boundary = ${fuel_surface_name}
    variable = c
    value_type = min
    execute_on = 'initial timestep_end'
    outputs = csv
  []
[]

# [VectorPostprocessors]
#   [surface_conditions]
#     type = SideValueSampler
#     variable = 'T D F c c_flux wastage_thickness'
#     boundary = ${fuel_surface_name}
#     sort_by = y
#     execute_on = 'initial timestep_end'
#     outputs = csv
#   []
# []

[Outputs]
  csv = true
  exodus = true
[]

(examples/metal_fuel/mechanistic_fcci/fcci.i)

# This example exercises the mechanistic Fuel-Cladding Chemical Interaction
# (FCCI) modeling approach for U-Zr and U-Pu-Zr metallic nuclear fuels. It is
# run as a SubApp, which is called by the combination of an existing assessment
# case and XXXX_multiapp.i.

# It is a collection of BISON classes and objects needed to apply a mechanistic
# FCCI model for U-Zr and U-Pu-Zr metallic nuclear fuels. It is designed to
# complement the modeling approaches adopted by the FIPD-powered X447 assessment
# cases and manually-developed X430 and IFR1 assessment cases. Thermomechanical
# behaviors are modeled in the existing assessment cases whereas lanthanide (Ln)
# transport, FCCI, and wastage growth are modeled in the SubApp. XXXX_multiapp.i
# then overrides the empirical FCCI model currently used in the assessments and
# replaces it with the mechanistic FCCI model. Examples of how to do this are
# included in the test and example specifications.

# Note that, in this model, c indicates the stable concentration of Lns. The
# model relies on an effective diffusion coefficient and flux terms informed by
# lower length scale modeling and simulations. Decay terms are included for
# illustration purposes but do not affect the solution.

# combined effective Ln production constant in mol/fission
ln_yield = 0.3 # atom/fission
avogadro = 6.0221e23 # atom/mol
production_constant = '${fparse ln_yield / avogadro}' # mol/fission

# combined effective Ln decay constant in 1/s
decay_constant = 0

# variable order, block and boundary names, and end time used in the assessment
order = placeholder
fuel_block_name = placeholder
fuel_surface_name = placeholder
end_time = placeholder

# fuel rod geometry and material properties used in the assessment
cladding_density = placeholder
fuel_outer_radius = placeholder
gap_thickness = placeholder

[GlobalParams]
  order = ${order}
  family = LAGRANGE
[]

[Problem]
  # nothing is being solved for on the cladding
  kernel_coverage_check = false
  material_coverage_check = false
[]

[Mesh]
[]

[Variables]
  [c] # stable Ln concentration in mol/m^3
    block = ${fuel_block_name}
  []
[]

[AuxVariables]
  [T]
    initial_condition = 298
  []
  [fission_rate]
    block = ${fuel_block_name}
    family = MONOMIAL
    order = CONSTANT
  []
  [porosity_aux]
    block = ${fuel_block_name}
    family = MONOMIAL
    order = CONSTANT
  []
  [sodium_logged_porosity_aux]
    block = ${fuel_block_name}
    family = MONOMIAL
    order = CONSTANT
  []
  [diffusivity]
    block = ${fuel_block_name}
    family = MONOMIAL
    order = CONSTANT
  []
  [dcdx]
    block = ${fuel_block_name}
    family = MONOMIAL
    order = CONSTANT
  []
  [c_flux]
    block = ${fuel_block_name}
    family = MONOMIAL
    order = CONSTANT
  []
[]

[AuxKernels]
  [diffusivity]
    type = MaterialRealAux
    boundary = ${fuel_surface_name}
    variable = diffusivity
    property = D
  []
  [dcdx]
    type = VariableGradientComponent
    boundary = ${fuel_surface_name}
    variable = dcdx
    gradient_variable = c
    component = x
  []
  [c_flux]
    type = ParsedAux
    boundary = ${fuel_surface_name}
    variable = c_flux
    coupled_variables = 'diffusivity dcdx'
    expression = '-diffusivity * dcdx'
  []
[]

[Kernels]
  [c_dt]
    type = TimeDerivative
    variable = c
  []
  [c_diffusion]
    type = MatDiffusion
    block = ${fuel_block_name}
    variable = c
    diffusivity = D
    args = 'c T'
  []
  [c_source]
    type = NeutronHeatSource
    block = ${fuel_block_name}
    variable = c
    fission_rate = fission_rate # fission/m^3-s
    energy_per_fission = ${production_constant} # mol/fission giving mol/m^3-s
  []
  [c_decay]
    type = Decay
    block = ${fuel_block_name}
    variable = c
    radioactive_decay_constant = ${decay_constant} # 1/s
  []
[]

[Materials]
  [porosity]
    type = ParsedMaterial
    block = ${fuel_block_name}
    property_name = porosity
    coupled_variables = porosity_aux
    expression = porosity_aux
  []
  [sodium_logged_porosity]
    type = ParsedMaterial
    block = ${fuel_block_name}
    property_name = sodium_logged_porosity
    coupled_variables = sodium_logged_porosity_aux
    expression = sodium_logged_porosity_aux
  []
  [diffusivity]
    # informed by lower length scale simulations
    type = UPuZrLanthanideDiffusivity
    block = ${fuel_block_name}
    property_name = D
    temperature = T
    porosity_name = porosity
    sodium_logged_porosity_name = sodium_logged_porosity
    outputs = exodus
    output_properties = D
  []
  [flux]
    # informed by lower length scale simulations
    type = UPuZrLanthanideFlux
    boundary = ${fuel_surface_name}
    property_name = F
    temperature = T
    concentration = c
    outputs = exodus
    output_properties = F
  []
  [wastage_thickness]
    # informed by lower length scale simulations
    type = UPuZrLanthanideWastage
    boundary = ${fuel_surface_name}
    cladding_density = ${cladding_density}
    fuel_outer_radius = ${fuel_outer_radius}
    gap_thickness =${gap_thickness}
    lanthanide_flux = F
    outputs = exodus
  []
[]

[BCs]
  [c_right]
    type = MatNeumannBC
    boundary = ${fuel_surface_name}
    variable = c
    boundary_material = F
    value = -1
  []
[]

[Executioner]
  type = Transient
  solve_type = PJFNK
  automatic_scaling = true
  compute_scaling_once = false
  petsc_options_iname = '-pc_type -pc_factor_mat_solver_package -pc_factor_shift_type -pc_factor_shift_amount'
  petsc_options_value = 'lu       superlu_dist                  NONZERO               1e-15'
  line_search = NONE
  l_max_its = 30
  l_tol = 1e-3
  nl_max_its = 30
  nl_rel_tol = 1e-10
  nl_abs_tol = 1e-6
  start_time = 0
  dt = 1e7
  end_time = ${end_time}
  verbose = true
[]

[Postprocessors]
  [c_in_fuel] # mol
    type = ElementIntegralVariablePostprocessor
    block = ${fuel_block_name}
    variable = c
    execute_on = 'initial timestep_end'
    outputs = 'console csv'
  []
  [fission_rate_total] # fission/s
    type = ElementIntegralVariablePostprocessor
    block = ${fuel_block_name}
    variable = fission_rate
    execute_on = 'initial timestep_end'
    outputs = csv
  []
  [fission_total] # fission
    type = TimeIntegratedPostprocessor
    value = fission_rate_total
    execute_on = 'initial timestep_end'
    outputs = csv
  []
  [c_produced] # mol
    type = LinearCombinationPostprocessor
    pp_names = fission_total
    pp_coefs = ${production_constant} # mol/fission giving mol
    execute_on = 'initial timestep_end'
    outputs = 'console csv'
  []
  [c_decay_rate] # mol/s
    type = LinearCombinationPostprocessor
    pp_names = c_in_fuel # mol
    pp_coefs = ${decay_constant} # 1/s
    execute_on = 'initial timestep_end'
    outputs = csv
  []
  [c_decayed] # mol
    type = TimeIntegratedPostprocessor
    value = c_decay_rate
    execute_on = 'initial timestep_end'
    outputs = csv
  []
  [c_reaction_rate] # mol/s
    type = SideDiffusiveFluxIntegral
    boundary = ${fuel_surface_name}
    variable = c
    diffusivity = D
    execute_on = 'initial timestep_end'
    outputs = csv
  []
  [c_reacted] # mol
    type = TimeIntegratedPostprocessor
    value = c_reaction_rate
    execute_on = 'initial timestep_end'
    outputs = 'console csv'
  []
  [c_flux_max]
    type = SideExtremeValue
    boundary = ${fuel_surface_name}
    variable = c_flux
    value_type = max
    execute_on = 'initial timestep_end'
    outputs = csv
  []
  [c_flux_min]
    type = SideExtremeValue
    boundary = ${fuel_surface_name}
    variable = c_flux
    value_type = min
    execute_on = 'initial timestep_end'
    outputs = csv
  []
  [wastage_thickness_max] # m
    type = ElementExtremeValue
    variable = wastage_thickness
    value_type = max
    execute_on = 'initial timestep_end'
    outputs = 'console csv'
  []
  [c_surface_max] # mol
    type = SideExtremeValue
    boundary = ${fuel_surface_name}
    variable = c
    value_type = max
    execute_on = 'initial timestep_end'
    outputs = csv
  []
  [c_surface_min] # mol
    type = SideExtremeValue
    boundary = ${fuel_surface_name}
    variable = c
    value_type = min
    execute_on = 'initial timestep_end'
    outputs = csv
  []
[]

# [VectorPostprocessors]
#   [surface_conditions]
#     type = SideValueSampler
#     variable = 'T D F c c_flux wastage_thickness'
#     boundary = ${fuel_surface_name}
#     sort_by = y
#     execute_on = 'initial timestep_end'
#     outputs = csv
#   []
# []

[Outputs]
  csv = true
  exodus = true
[]

(examples/metal_fuel/mechanistic_fcci/fcci.i)

# This example exercises the mechanistic Fuel-Cladding Chemical Interaction
# (FCCI) modeling approach for U-Zr and U-Pu-Zr metallic nuclear fuels. It is
# run as a SubApp, which is called by the combination of an existing assessment
# case and XXXX_multiapp.i.

# It is a collection of BISON classes and objects needed to apply a mechanistic
# FCCI model for U-Zr and U-Pu-Zr metallic nuclear fuels. It is designed to
# complement the modeling approaches adopted by the FIPD-powered X447 assessment
# cases and manually-developed X430 and IFR1 assessment cases. Thermomechanical
# behaviors are modeled in the existing assessment cases whereas lanthanide (Ln)
# transport, FCCI, and wastage growth are modeled in the SubApp. XXXX_multiapp.i
# then overrides the empirical FCCI model currently used in the assessments and
# replaces it with the mechanistic FCCI model. Examples of how to do this are
# included in the test and example specifications.

# Note that, in this model, c indicates the stable concentration of Lns. The
# model relies on an effective diffusion coefficient and flux terms informed by
# lower length scale modeling and simulations. Decay terms are included for
# illustration purposes but do not affect the solution.

# combined effective Ln production constant in mol/fission
ln_yield = 0.3 # atom/fission
avogadro = 6.0221e23 # atom/mol
production_constant = '${fparse ln_yield / avogadro}' # mol/fission

# combined effective Ln decay constant in 1/s
decay_constant = 0

# variable order, block and boundary names, and end time used in the assessment
order = placeholder
fuel_block_name = placeholder
fuel_surface_name = placeholder
end_time = placeholder

# fuel rod geometry and material properties used in the assessment
cladding_density = placeholder
fuel_outer_radius = placeholder
gap_thickness = placeholder

[GlobalParams]
  order = ${order}
  family = LAGRANGE
[]

[Problem]
  # nothing is being solved for on the cladding
  kernel_coverage_check = false
  material_coverage_check = false
[]

[Mesh]
[]

[Variables]
  [c] # stable Ln concentration in mol/m^3
    block = ${fuel_block_name}
  []
[]

[AuxVariables]
  [T]
    initial_condition = 298
  []
  [fission_rate]
    block = ${fuel_block_name}
    family = MONOMIAL
    order = CONSTANT
  []
  [porosity_aux]
    block = ${fuel_block_name}
    family = MONOMIAL
    order = CONSTANT
  []
  [sodium_logged_porosity_aux]
    block = ${fuel_block_name}
    family = MONOMIAL
    order = CONSTANT
  []
  [diffusivity]
    block = ${fuel_block_name}
    family = MONOMIAL
    order = CONSTANT
  []
  [dcdx]
    block = ${fuel_block_name}
    family = MONOMIAL
    order = CONSTANT
  []
  [c_flux]
    block = ${fuel_block_name}
    family = MONOMIAL
    order = CONSTANT
  []
[]

[AuxKernels]
  [diffusivity]
    type = MaterialRealAux
    boundary = ${fuel_surface_name}
    variable = diffusivity
    property = D
  []
  [dcdx]
    type = VariableGradientComponent
    boundary = ${fuel_surface_name}
    variable = dcdx
    gradient_variable = c
    component = x
  []
  [c_flux]
    type = ParsedAux
    boundary = ${fuel_surface_name}
    variable = c_flux
    coupled_variables = 'diffusivity dcdx'
    expression = '-diffusivity * dcdx'
  []
[]

[Kernels]
  [c_dt]
    type = TimeDerivative
    variable = c
  []
  [c_diffusion]
    type = MatDiffusion
    block = ${fuel_block_name}
    variable = c
    diffusivity = D
    args = 'c T'
  []
  [c_source]
    type = NeutronHeatSource
    block = ${fuel_block_name}
    variable = c
    fission_rate = fission_rate # fission/m^3-s
    energy_per_fission = ${production_constant} # mol/fission giving mol/m^3-s
  []
  [c_decay]
    type = Decay
    block = ${fuel_block_name}
    variable = c
    radioactive_decay_constant = ${decay_constant} # 1/s
  []
[]

[Materials]
  [porosity]
    type = ParsedMaterial
    block = ${fuel_block_name}
    property_name = porosity
    coupled_variables = porosity_aux
    expression = porosity_aux
  []
  [sodium_logged_porosity]
    type = ParsedMaterial
    block = ${fuel_block_name}
    property_name = sodium_logged_porosity
    coupled_variables = sodium_logged_porosity_aux
    expression = sodium_logged_porosity_aux
  []
  [diffusivity]
    # informed by lower length scale simulations
    type = UPuZrLanthanideDiffusivity
    block = ${fuel_block_name}
    property_name = D
    temperature = T
    porosity_name = porosity
    sodium_logged_porosity_name = sodium_logged_porosity
    outputs = exodus
    output_properties = D
  []
  [flux]
    # informed by lower length scale simulations
    type = UPuZrLanthanideFlux
    boundary = ${fuel_surface_name}
    property_name = F
    temperature = T
    concentration = c
    outputs = exodus
    output_properties = F
  []
  [wastage_thickness]
    # informed by lower length scale simulations
    type = UPuZrLanthanideWastage
    boundary = ${fuel_surface_name}
    cladding_density = ${cladding_density}
    fuel_outer_radius = ${fuel_outer_radius}
    gap_thickness =${gap_thickness}
    lanthanide_flux = F
    outputs = exodus
  []
[]

[BCs]
  [c_right]
    type = MatNeumannBC
    boundary = ${fuel_surface_name}
    variable = c
    boundary_material = F
    value = -1
  []
[]

[Executioner]
  type = Transient
  solve_type = PJFNK
  automatic_scaling = true
  compute_scaling_once = false
  petsc_options_iname = '-pc_type -pc_factor_mat_solver_package -pc_factor_shift_type -pc_factor_shift_amount'
  petsc_options_value = 'lu       superlu_dist                  NONZERO               1e-15'
  line_search = NONE
  l_max_its = 30
  l_tol = 1e-3
  nl_max_its = 30
  nl_rel_tol = 1e-10
  nl_abs_tol = 1e-6
  start_time = 0
  dt = 1e7
  end_time = ${end_time}
  verbose = true
[]

[Postprocessors]
  [c_in_fuel] # mol
    type = ElementIntegralVariablePostprocessor
    block = ${fuel_block_name}
    variable = c
    execute_on = 'initial timestep_end'
    outputs = 'console csv'
  []
  [fission_rate_total] # fission/s
    type = ElementIntegralVariablePostprocessor
    block = ${fuel_block_name}
    variable = fission_rate
    execute_on = 'initial timestep_end'
    outputs = csv
  []
  [fission_total] # fission
    type = TimeIntegratedPostprocessor
    value = fission_rate_total
    execute_on = 'initial timestep_end'
    outputs = csv
  []
  [c_produced] # mol
    type = LinearCombinationPostprocessor
    pp_names = fission_total
    pp_coefs = ${production_constant} # mol/fission giving mol
    execute_on = 'initial timestep_end'
    outputs = 'console csv'
  []
  [c_decay_rate] # mol/s
    type = LinearCombinationPostprocessor
    pp_names = c_in_fuel # mol
    pp_coefs = ${decay_constant} # 1/s
    execute_on = 'initial timestep_end'
    outputs = csv
  []
  [c_decayed] # mol
    type = TimeIntegratedPostprocessor
    value = c_decay_rate
    execute_on = 'initial timestep_end'
    outputs = csv
  []
  [c_reaction_rate] # mol/s
    type = SideDiffusiveFluxIntegral
    boundary = ${fuel_surface_name}
    variable = c
    diffusivity = D
    execute_on = 'initial timestep_end'
    outputs = csv
  []
  [c_reacted] # mol
    type = TimeIntegratedPostprocessor
    value = c_reaction_rate
    execute_on = 'initial timestep_end'
    outputs = 'console csv'
  []
  [c_flux_max]
    type = SideExtremeValue
    boundary = ${fuel_surface_name}
    variable = c_flux
    value_type = max
    execute_on = 'initial timestep_end'
    outputs = csv
  []
  [c_flux_min]
    type = SideExtremeValue
    boundary = ${fuel_surface_name}
    variable = c_flux
    value_type = min
    execute_on = 'initial timestep_end'
    outputs = csv
  []
  [wastage_thickness_max] # m
    type = ElementExtremeValue
    variable = wastage_thickness
    value_type = max
    execute_on = 'initial timestep_end'
    outputs = 'console csv'
  []
  [c_surface_max] # mol
    type = SideExtremeValue
    boundary = ${fuel_surface_name}
    variable = c
    value_type = max
    execute_on = 'initial timestep_end'
    outputs = csv
  []
  [c_surface_min] # mol
    type = SideExtremeValue
    boundary = ${fuel_surface_name}
    variable = c
    value_type = min
    execute_on = 'initial timestep_end'
    outputs = csv
  []
[]

# [VectorPostprocessors]
#   [surface_conditions]
#     type = SideValueSampler
#     variable = 'T D F c c_flux wastage_thickness'
#     boundary = ${fuel_surface_name}
#     sort_by = y
#     execute_on = 'initial timestep_end'
#     outputs = csv
#   []
# []

[Outputs]
  csv = true
  exodus = true
[]

(examples/metal_fuel/mechanistic_fcci/fcci.i)

# This example exercises the mechanistic Fuel-Cladding Chemical Interaction
# (FCCI) modeling approach for U-Zr and U-Pu-Zr metallic nuclear fuels. It is
# run as a SubApp, which is called by the combination of an existing assessment
# case and XXXX_multiapp.i.

# It is a collection of BISON classes and objects needed to apply a mechanistic
# FCCI model for U-Zr and U-Pu-Zr metallic nuclear fuels. It is designed to
# complement the modeling approaches adopted by the FIPD-powered X447 assessment
# cases and manually-developed X430 and IFR1 assessment cases. Thermomechanical
# behaviors are modeled in the existing assessment cases whereas lanthanide (Ln)
# transport, FCCI, and wastage growth are modeled in the SubApp. XXXX_multiapp.i
# then overrides the empirical FCCI model currently used in the assessments and
# replaces it with the mechanistic FCCI model. Examples of how to do this are
# included in the test and example specifications.

# Note that, in this model, c indicates the stable concentration of Lns. The
# model relies on an effective diffusion coefficient and flux terms informed by
# lower length scale modeling and simulations. Decay terms are included for
# illustration purposes but do not affect the solution.

# combined effective Ln production constant in mol/fission
ln_yield = 0.3 # atom/fission
avogadro = 6.0221e23 # atom/mol
production_constant = '${fparse ln_yield / avogadro}' # mol/fission

# combined effective Ln decay constant in 1/s
decay_constant = 0

# variable order, block and boundary names, and end time used in the assessment
order = placeholder
fuel_block_name = placeholder
fuel_surface_name = placeholder
end_time = placeholder

# fuel rod geometry and material properties used in the assessment
cladding_density = placeholder
fuel_outer_radius = placeholder
gap_thickness = placeholder

[GlobalParams]
  order = ${order}
  family = LAGRANGE
[]

[Problem]
  # nothing is being solved for on the cladding
  kernel_coverage_check = false
  material_coverage_check = false
[]

[Mesh]
[]

[Variables]
  [c] # stable Ln concentration in mol/m^3
    block = ${fuel_block_name}
  []
[]

[AuxVariables]
  [T]
    initial_condition = 298
  []
  [fission_rate]
    block = ${fuel_block_name}
    family = MONOMIAL
    order = CONSTANT
  []
  [porosity_aux]
    block = ${fuel_block_name}
    family = MONOMIAL
    order = CONSTANT
  []
  [sodium_logged_porosity_aux]
    block = ${fuel_block_name}
    family = MONOMIAL
    order = CONSTANT
  []
  [diffusivity]
    block = ${fuel_block_name}
    family = MONOMIAL
    order = CONSTANT
  []
  [dcdx]
    block = ${fuel_block_name}
    family = MONOMIAL
    order = CONSTANT
  []
  [c_flux]
    block = ${fuel_block_name}
    family = MONOMIAL
    order = CONSTANT
  []
[]

[AuxKernels]
  [diffusivity]
    type = MaterialRealAux
    boundary = ${fuel_surface_name}
    variable = diffusivity
    property = D
  []
  [dcdx]
    type = VariableGradientComponent
    boundary = ${fuel_surface_name}
    variable = dcdx
    gradient_variable = c
    component = x
  []
  [c_flux]
    type = ParsedAux
    boundary = ${fuel_surface_name}
    variable = c_flux
    coupled_variables = 'diffusivity dcdx'
    expression = '-diffusivity * dcdx'
  []
[]

[Kernels]
  [c_dt]
    type = TimeDerivative
    variable = c
  []
  [c_diffusion]
    type = MatDiffusion
    block = ${fuel_block_name}
    variable = c
    diffusivity = D
    args = 'c T'
  []
  [c_source]
    type = NeutronHeatSource
    block = ${fuel_block_name}
    variable = c
    fission_rate = fission_rate # fission/m^3-s
    energy_per_fission = ${production_constant} # mol/fission giving mol/m^3-s
  []
  [c_decay]
    type = Decay
    block = ${fuel_block_name}
    variable = c
    radioactive_decay_constant = ${decay_constant} # 1/s
  []
[]

[Materials]
  [porosity]
    type = ParsedMaterial
    block = ${fuel_block_name}
    property_name = porosity
    coupled_variables = porosity_aux
    expression = porosity_aux
  []
  [sodium_logged_porosity]
    type = ParsedMaterial
    block = ${fuel_block_name}
    property_name = sodium_logged_porosity
    coupled_variables = sodium_logged_porosity_aux
    expression = sodium_logged_porosity_aux
  []
  [diffusivity]
    # informed by lower length scale simulations
    type = UPuZrLanthanideDiffusivity
    block = ${fuel_block_name}
    property_name = D
    temperature = T
    porosity_name = porosity
    sodium_logged_porosity_name = sodium_logged_porosity
    outputs = exodus
    output_properties = D
  []
  [flux]
    # informed by lower length scale simulations
    type = UPuZrLanthanideFlux
    boundary = ${fuel_surface_name}
    property_name = F
    temperature = T
    concentration = c
    outputs = exodus
    output_properties = F
  []
  [wastage_thickness]
    # informed by lower length scale simulations
    type = UPuZrLanthanideWastage
    boundary = ${fuel_surface_name}
    cladding_density = ${cladding_density}
    fuel_outer_radius = ${fuel_outer_radius}
    gap_thickness =${gap_thickness}
    lanthanide_flux = F
    outputs = exodus
  []
[]

[BCs]
  [c_right]
    type = MatNeumannBC
    boundary = ${fuel_surface_name}
    variable = c
    boundary_material = F
    value = -1
  []
[]

[Executioner]
  type = Transient
  solve_type = PJFNK
  automatic_scaling = true
  compute_scaling_once = false
  petsc_options_iname = '-pc_type -pc_factor_mat_solver_package -pc_factor_shift_type -pc_factor_shift_amount'
  petsc_options_value = 'lu       superlu_dist                  NONZERO               1e-15'
  line_search = NONE
  l_max_its = 30
  l_tol = 1e-3
  nl_max_its = 30
  nl_rel_tol = 1e-10
  nl_abs_tol = 1e-6
  start_time = 0
  dt = 1e7
  end_time = ${end_time}
  verbose = true
[]

[Postprocessors]
  [c_in_fuel] # mol
    type = ElementIntegralVariablePostprocessor
    block = ${fuel_block_name}
    variable = c
    execute_on = 'initial timestep_end'
    outputs = 'console csv'
  []
  [fission_rate_total] # fission/s
    type = ElementIntegralVariablePostprocessor
    block = ${fuel_block_name}
    variable = fission_rate
    execute_on = 'initial timestep_end'
    outputs = csv
  []
  [fission_total] # fission
    type = TimeIntegratedPostprocessor
    value = fission_rate_total
    execute_on = 'initial timestep_end'
    outputs = csv
  []
  [c_produced] # mol
    type = LinearCombinationPostprocessor
    pp_names = fission_total
    pp_coefs = ${production_constant} # mol/fission giving mol
    execute_on = 'initial timestep_end'
    outputs = 'console csv'
  []
  [c_decay_rate] # mol/s
    type = LinearCombinationPostprocessor
    pp_names = c_in_fuel # mol
    pp_coefs = ${decay_constant} # 1/s
    execute_on = 'initial timestep_end'
    outputs = csv
  []
  [c_decayed] # mol
    type = TimeIntegratedPostprocessor
    value = c_decay_rate
    execute_on = 'initial timestep_end'
    outputs = csv
  []
  [c_reaction_rate] # mol/s
    type = SideDiffusiveFluxIntegral
    boundary = ${fuel_surface_name}
    variable = c
    diffusivity = D
    execute_on = 'initial timestep_end'
    outputs = csv
  []
  [c_reacted] # mol
    type = TimeIntegratedPostprocessor
    value = c_reaction_rate
    execute_on = 'initial timestep_end'
    outputs = 'console csv'
  []
  [c_flux_max]
    type = SideExtremeValue
    boundary = ${fuel_surface_name}
    variable = c_flux
    value_type = max
    execute_on = 'initial timestep_end'
    outputs = csv
  []
  [c_flux_min]
    type = SideExtremeValue
    boundary = ${fuel_surface_name}
    variable = c_flux
    value_type = min
    execute_on = 'initial timestep_end'
    outputs = csv
  []
  [wastage_thickness_max] # m
    type = ElementExtremeValue
    variable = wastage_thickness
    value_type = max
    execute_on = 'initial timestep_end'
    outputs = 'console csv'
  []
  [c_surface_max] # mol
    type = SideExtremeValue
    boundary = ${fuel_surface_name}
    variable = c
    value_type = max
    execute_on = 'initial timestep_end'
    outputs = csv
  []
  [c_surface_min] # mol
    type = SideExtremeValue
    boundary = ${fuel_surface_name}
    variable = c
    value_type = min
    execute_on = 'initial timestep_end'
    outputs = csv
  []
[]

# [VectorPostprocessors]
#   [surface_conditions]
#     type = SideValueSampler
#     variable = 'T D F c c_flux wastage_thickness'
#     boundary = ${fuel_surface_name}
#     sort_by = y
#     execute_on = 'initial timestep_end'
#     outputs = csv
#   []
# []

[Outputs]
  csv = true
  exodus = true
[]

(examples/metal_fuel/mechanistic_fcci/fcci.i)

# This example exercises the mechanistic Fuel-Cladding Chemical Interaction
# (FCCI) modeling approach for U-Zr and U-Pu-Zr metallic nuclear fuels. It is
# run as a SubApp, which is called by the combination of an existing assessment
# case and XXXX_multiapp.i.

# It is a collection of BISON classes and objects needed to apply a mechanistic
# FCCI model for U-Zr and U-Pu-Zr metallic nuclear fuels. It is designed to
# complement the modeling approaches adopted by the FIPD-powered X447 assessment
# cases and manually-developed X430 and IFR1 assessment cases. Thermomechanical
# behaviors are modeled in the existing assessment cases whereas lanthanide (Ln)
# transport, FCCI, and wastage growth are modeled in the SubApp. XXXX_multiapp.i
# then overrides the empirical FCCI model currently used in the assessments and
# replaces it with the mechanistic FCCI model. Examples of how to do this are
# included in the test and example specifications.

# Note that, in this model, c indicates the stable concentration of Lns. The
# model relies on an effective diffusion coefficient and flux terms informed by
# lower length scale modeling and simulations. Decay terms are included for
# illustration purposes but do not affect the solution.

# combined effective Ln production constant in mol/fission
ln_yield = 0.3 # atom/fission
avogadro = 6.0221e23 # atom/mol
production_constant = '${fparse ln_yield / avogadro}' # mol/fission

# combined effective Ln decay constant in 1/s
decay_constant = 0

# variable order, block and boundary names, and end time used in the assessment
order = placeholder
fuel_block_name = placeholder
fuel_surface_name = placeholder
end_time = placeholder

# fuel rod geometry and material properties used in the assessment
cladding_density = placeholder
fuel_outer_radius = placeholder
gap_thickness = placeholder

[GlobalParams]
  order = ${order}
  family = LAGRANGE
[]

[Problem]
  # nothing is being solved for on the cladding
  kernel_coverage_check = false
  material_coverage_check = false
[]

[Mesh]
[]

[Variables]
  [c] # stable Ln concentration in mol/m^3
    block = ${fuel_block_name}
  []
[]

[AuxVariables]
  [T]
    initial_condition = 298
  []
  [fission_rate]
    block = ${fuel_block_name}
    family = MONOMIAL
    order = CONSTANT
  []
  [porosity_aux]
    block = ${fuel_block_name}
    family = MONOMIAL
    order = CONSTANT
  []
  [sodium_logged_porosity_aux]
    block = ${fuel_block_name}
    family = MONOMIAL
    order = CONSTANT
  []
  [diffusivity]
    block = ${fuel_block_name}
    family = MONOMIAL
    order = CONSTANT
  []
  [dcdx]
    block = ${fuel_block_name}
    family = MONOMIAL
    order = CONSTANT
  []
  [c_flux]
    block = ${fuel_block_name}
    family = MONOMIAL
    order = CONSTANT
  []
[]

[AuxKernels]
  [diffusivity]
    type = MaterialRealAux
    boundary = ${fuel_surface_name}
    variable = diffusivity
    property = D
  []
  [dcdx]
    type = VariableGradientComponent
    boundary = ${fuel_surface_name}
    variable = dcdx
    gradient_variable = c
    component = x
  []
  [c_flux]
    type = ParsedAux
    boundary = ${fuel_surface_name}
    variable = c_flux
    coupled_variables = 'diffusivity dcdx'
    expression = '-diffusivity * dcdx'
  []
[]

[Kernels]
  [c_dt]
    type = TimeDerivative
    variable = c
  []
  [c_diffusion]
    type = MatDiffusion
    block = ${fuel_block_name}
    variable = c
    diffusivity = D
    args = 'c T'
  []
  [c_source]
    type = NeutronHeatSource
    block = ${fuel_block_name}
    variable = c
    fission_rate = fission_rate # fission/m^3-s
    energy_per_fission = ${production_constant} # mol/fission giving mol/m^3-s
  []
  [c_decay]
    type = Decay
    block = ${fuel_block_name}
    variable = c
    radioactive_decay_constant = ${decay_constant} # 1/s
  []
[]

[Materials]
  [porosity]
    type = ParsedMaterial
    block = ${fuel_block_name}
    property_name = porosity
    coupled_variables = porosity_aux
    expression = porosity_aux
  []
  [sodium_logged_porosity]
    type = ParsedMaterial
    block = ${fuel_block_name}
    property_name = sodium_logged_porosity
    coupled_variables = sodium_logged_porosity_aux
    expression = sodium_logged_porosity_aux
  []
  [diffusivity]
    # informed by lower length scale simulations
    type = UPuZrLanthanideDiffusivity
    block = ${fuel_block_name}
    property_name = D
    temperature = T
    porosity_name = porosity
    sodium_logged_porosity_name = sodium_logged_porosity
    outputs = exodus
    output_properties = D
  []
  [flux]
    # informed by lower length scale simulations
    type = UPuZrLanthanideFlux
    boundary = ${fuel_surface_name}
    property_name = F
    temperature = T
    concentration = c
    outputs = exodus
    output_properties = F
  []
  [wastage_thickness]
    # informed by lower length scale simulations
    type = UPuZrLanthanideWastage
    boundary = ${fuel_surface_name}
    cladding_density = ${cladding_density}
    fuel_outer_radius = ${fuel_outer_radius}
    gap_thickness =${gap_thickness}
    lanthanide_flux = F
    outputs = exodus
  []
[]

[BCs]
  [c_right]
    type = MatNeumannBC
    boundary = ${fuel_surface_name}
    variable = c
    boundary_material = F
    value = -1
  []
[]

[Executioner]
  type = Transient
  solve_type = PJFNK
  automatic_scaling = true
  compute_scaling_once = false
  petsc_options_iname = '-pc_type -pc_factor_mat_solver_package -pc_factor_shift_type -pc_factor_shift_amount'
  petsc_options_value = 'lu       superlu_dist                  NONZERO               1e-15'
  line_search = NONE
  l_max_its = 30
  l_tol = 1e-3
  nl_max_its = 30
  nl_rel_tol = 1e-10
  nl_abs_tol = 1e-6
  start_time = 0
  dt = 1e7
  end_time = ${end_time}
  verbose = true
[]

[Postprocessors]
  [c_in_fuel] # mol
    type = ElementIntegralVariablePostprocessor
    block = ${fuel_block_name}
    variable = c
    execute_on = 'initial timestep_end'
    outputs = 'console csv'
  []
  [fission_rate_total] # fission/s
    type = ElementIntegralVariablePostprocessor
    block = ${fuel_block_name}
    variable = fission_rate
    execute_on = 'initial timestep_end'
    outputs = csv
  []
  [fission_total] # fission
    type = TimeIntegratedPostprocessor
    value = fission_rate_total
    execute_on = 'initial timestep_end'
    outputs = csv
  []
  [c_produced] # mol
    type = LinearCombinationPostprocessor
    pp_names = fission_total
    pp_coefs = ${production_constant} # mol/fission giving mol
    execute_on = 'initial timestep_end'
    outputs = 'console csv'
  []
  [c_decay_rate] # mol/s
    type = LinearCombinationPostprocessor
    pp_names = c_in_fuel # mol
    pp_coefs = ${decay_constant} # 1/s
    execute_on = 'initial timestep_end'
    outputs = csv
  []
  [c_decayed] # mol
    type = TimeIntegratedPostprocessor
    value = c_decay_rate
    execute_on = 'initial timestep_end'
    outputs = csv
  []
  [c_reaction_rate] # mol/s
    type = SideDiffusiveFluxIntegral
    boundary = ${fuel_surface_name}
    variable = c
    diffusivity = D
    execute_on = 'initial timestep_end'
    outputs = csv
  []
  [c_reacted] # mol
    type = TimeIntegratedPostprocessor
    value = c_reaction_rate
    execute_on = 'initial timestep_end'
    outputs = 'console csv'
  []
  [c_flux_max]
    type = SideExtremeValue
    boundary = ${fuel_surface_name}
    variable = c_flux
    value_type = max
    execute_on = 'initial timestep_end'
    outputs = csv
  []
  [c_flux_min]
    type = SideExtremeValue
    boundary = ${fuel_surface_name}
    variable = c_flux
    value_type = min
    execute_on = 'initial timestep_end'
    outputs = csv
  []
  [wastage_thickness_max] # m
    type = ElementExtremeValue
    variable = wastage_thickness
    value_type = max
    execute_on = 'initial timestep_end'
    outputs = 'console csv'
  []
  [c_surface_max] # mol
    type = SideExtremeValue
    boundary = ${fuel_surface_name}
    variable = c
    value_type = max
    execute_on = 'initial timestep_end'
    outputs = csv
  []
  [c_surface_min] # mol
    type = SideExtremeValue
    boundary = ${fuel_surface_name}
    variable = c
    value_type = min
    execute_on = 'initial timestep_end'
    outputs = csv
  []
[]

# [VectorPostprocessors]
#   [surface_conditions]
#     type = SideValueSampler
#     variable = 'T D F c c_flux wastage_thickness'
#     boundary = ${fuel_surface_name}
#     sort_by = y
#     execute_on = 'initial timestep_end'
#     outputs = csv
#   []
# []

[Outputs]
  csv = true
  exodus = true
[]

(examples/metal_fuel/mechanistic_fcci/fcci.i)

# This example exercises the mechanistic Fuel-Cladding Chemical Interaction
# (FCCI) modeling approach for U-Zr and U-Pu-Zr metallic nuclear fuels. It is
# run as a SubApp, which is called by the combination of an existing assessment
# case and XXXX_multiapp.i.

# It is a collection of BISON classes and objects needed to apply a mechanistic
# FCCI model for U-Zr and U-Pu-Zr metallic nuclear fuels. It is designed to
# complement the modeling approaches adopted by the FIPD-powered X447 assessment
# cases and manually-developed X430 and IFR1 assessment cases. Thermomechanical
# behaviors are modeled in the existing assessment cases whereas lanthanide (Ln)
# transport, FCCI, and wastage growth are modeled in the SubApp. XXXX_multiapp.i
# then overrides the empirical FCCI model currently used in the assessments and
# replaces it with the mechanistic FCCI model. Examples of how to do this are
# included in the test and example specifications.

# Note that, in this model, c indicates the stable concentration of Lns. The
# model relies on an effective diffusion coefficient and flux terms informed by
# lower length scale modeling and simulations. Decay terms are included for
# illustration purposes but do not affect the solution.

# combined effective Ln production constant in mol/fission
ln_yield = 0.3 # atom/fission
avogadro = 6.0221e23 # atom/mol
production_constant = '${fparse ln_yield / avogadro}' # mol/fission

# combined effective Ln decay constant in 1/s
decay_constant = 0

# variable order, block and boundary names, and end time used in the assessment
order = placeholder
fuel_block_name = placeholder
fuel_surface_name = placeholder
end_time = placeholder

# fuel rod geometry and material properties used in the assessment
cladding_density = placeholder
fuel_outer_radius = placeholder
gap_thickness = placeholder

[GlobalParams]
  order = ${order}
  family = LAGRANGE
[]

[Problem]
  # nothing is being solved for on the cladding
  kernel_coverage_check = false
  material_coverage_check = false
[]

[Mesh]
[]

[Variables]
  [c] # stable Ln concentration in mol/m^3
    block = ${fuel_block_name}
  []
[]

[AuxVariables]
  [T]
    initial_condition = 298
  []
  [fission_rate]
    block = ${fuel_block_name}
    family = MONOMIAL
    order = CONSTANT
  []
  [porosity_aux]
    block = ${fuel_block_name}
    family = MONOMIAL
    order = CONSTANT
  []
  [sodium_logged_porosity_aux]
    block = ${fuel_block_name}
    family = MONOMIAL
    order = CONSTANT
  []
  [diffusivity]
    block = ${fuel_block_name}
    family = MONOMIAL
    order = CONSTANT
  []
  [dcdx]
    block = ${fuel_block_name}
    family = MONOMIAL
    order = CONSTANT
  []
  [c_flux]
    block = ${fuel_block_name}
    family = MONOMIAL
    order = CONSTANT
  []
[]

[AuxKernels]
  [diffusivity]
    type = MaterialRealAux
    boundary = ${fuel_surface_name}
    variable = diffusivity
    property = D
  []
  [dcdx]
    type = VariableGradientComponent
    boundary = ${fuel_surface_name}
    variable = dcdx
    gradient_variable = c
    component = x
  []
  [c_flux]
    type = ParsedAux
    boundary = ${fuel_surface_name}
    variable = c_flux
    coupled_variables = 'diffusivity dcdx'
    expression = '-diffusivity * dcdx'
  []
[]

[Kernels]
  [c_dt]
    type = TimeDerivative
    variable = c
  []
  [c_diffusion]
    type = MatDiffusion
    block = ${fuel_block_name}
    variable = c
    diffusivity = D
    args = 'c T'
  []
  [c_source]
    type = NeutronHeatSource
    block = ${fuel_block_name}
    variable = c
    fission_rate = fission_rate # fission/m^3-s
    energy_per_fission = ${production_constant} # mol/fission giving mol/m^3-s
  []
  [c_decay]
    type = Decay
    block = ${fuel_block_name}
    variable = c
    radioactive_decay_constant = ${decay_constant} # 1/s
  []
[]

[Materials]
  [porosity]
    type = ParsedMaterial
    block = ${fuel_block_name}
    property_name = porosity
    coupled_variables = porosity_aux
    expression = porosity_aux
  []
  [sodium_logged_porosity]
    type = ParsedMaterial
    block = ${fuel_block_name}
    property_name = sodium_logged_porosity
    coupled_variables = sodium_logged_porosity_aux
    expression = sodium_logged_porosity_aux
  []
  [diffusivity]
    # informed by lower length scale simulations
    type = UPuZrLanthanideDiffusivity
    block = ${fuel_block_name}
    property_name = D
    temperature = T
    porosity_name = porosity
    sodium_logged_porosity_name = sodium_logged_porosity
    outputs = exodus
    output_properties = D
  []
  [flux]
    # informed by lower length scale simulations
    type = UPuZrLanthanideFlux
    boundary = ${fuel_surface_name}
    property_name = F
    temperature = T
    concentration = c
    outputs = exodus
    output_properties = F
  []
  [wastage_thickness]
    # informed by lower length scale simulations
    type = UPuZrLanthanideWastage
    boundary = ${fuel_surface_name}
    cladding_density = ${cladding_density}
    fuel_outer_radius = ${fuel_outer_radius}
    gap_thickness =${gap_thickness}
    lanthanide_flux = F
    outputs = exodus
  []
[]

[BCs]
  [c_right]
    type = MatNeumannBC
    boundary = ${fuel_surface_name}
    variable = c
    boundary_material = F
    value = -1
  []
[]

[Executioner]
  type = Transient
  solve_type = PJFNK
  automatic_scaling = true
  compute_scaling_once = false
  petsc_options_iname = '-pc_type -pc_factor_mat_solver_package -pc_factor_shift_type -pc_factor_shift_amount'
  petsc_options_value = 'lu       superlu_dist                  NONZERO               1e-15'
  line_search = NONE
  l_max_its = 30
  l_tol = 1e-3
  nl_max_its = 30
  nl_rel_tol = 1e-10
  nl_abs_tol = 1e-6
  start_time = 0
  dt = 1e7
  end_time = ${end_time}
  verbose = true
[]

[Postprocessors]
  [c_in_fuel] # mol
    type = ElementIntegralVariablePostprocessor
    block = ${fuel_block_name}
    variable = c
    execute_on = 'initial timestep_end'
    outputs = 'console csv'
  []
  [fission_rate_total] # fission/s
    type = ElementIntegralVariablePostprocessor
    block = ${fuel_block_name}
    variable = fission_rate
    execute_on = 'initial timestep_end'
    outputs = csv
  []
  [fission_total] # fission
    type = TimeIntegratedPostprocessor
    value = fission_rate_total
    execute_on = 'initial timestep_end'
    outputs = csv
  []
  [c_produced] # mol
    type = LinearCombinationPostprocessor
    pp_names = fission_total
    pp_coefs = ${production_constant} # mol/fission giving mol
    execute_on = 'initial timestep_end'
    outputs = 'console csv'
  []
  [c_decay_rate] # mol/s
    type = LinearCombinationPostprocessor
    pp_names = c_in_fuel # mol
    pp_coefs = ${decay_constant} # 1/s
    execute_on = 'initial timestep_end'
    outputs = csv
  []
  [c_decayed] # mol
    type = TimeIntegratedPostprocessor
    value = c_decay_rate
    execute_on = 'initial timestep_end'
    outputs = csv
  []
  [c_reaction_rate] # mol/s
    type = SideDiffusiveFluxIntegral
    boundary = ${fuel_surface_name}
    variable = c
    diffusivity = D
    execute_on = 'initial timestep_end'
    outputs = csv
  []
  [c_reacted] # mol
    type = TimeIntegratedPostprocessor
    value = c_reaction_rate
    execute_on = 'initial timestep_end'
    outputs = 'console csv'
  []
  [c_flux_max]
    type = SideExtremeValue
    boundary = ${fuel_surface_name}
    variable = c_flux
    value_type = max
    execute_on = 'initial timestep_end'
    outputs = csv
  []
  [c_flux_min]
    type = SideExtremeValue
    boundary = ${fuel_surface_name}
    variable = c_flux
    value_type = min
    execute_on = 'initial timestep_end'
    outputs = csv
  []
  [wastage_thickness_max] # m
    type = ElementExtremeValue
    variable = wastage_thickness
    value_type = max
    execute_on = 'initial timestep_end'
    outputs = 'console csv'
  []
  [c_surface_max] # mol
    type = SideExtremeValue
    boundary = ${fuel_surface_name}
    variable = c
    value_type = max
    execute_on = 'initial timestep_end'
    outputs = csv
  []
  [c_surface_min] # mol
    type = SideExtremeValue
    boundary = ${fuel_surface_name}
    variable = c
    value_type = min
    execute_on = 'initial timestep_end'
    outputs = csv
  []
[]

# [VectorPostprocessors]
#   [surface_conditions]
#     type = SideValueSampler
#     variable = 'T D F c c_flux wastage_thickness'
#     boundary = ${fuel_surface_name}
#     sort_by = y
#     execute_on = 'initial timestep_end'
#     outputs = csv
#   []
# []

[Outputs]
  csv = true
  exodus = true
[]

(test/tests/upuzr_lanthanide_wastage/test.i)

cladding_stoichiometry = 18
lanthanide_stoichiometry = 3
cladding_molar_mass = 6e-2
cladding_density = 7e3
fuel_outer_radius = 2e-3
gap_thickness = 4e-4
thickness_variability_factor = 3

[Mesh]
  coord_type = RZ
  [mesh]
    type = GeneratedMeshGenerator
    dim = 1
    nx = 1
  []
[]

[Variables]
  [test]
  []
[]

[Kernels]
  [test]
    type = TimeDerivative
    variable = test
  []
[]

[Functions]
  [lanthanide_flux]
    type = ParsedFunction
    expression = '5 - t'
  []
  [wastage_thickness_exact]
    type = ParsedFunction
    symbol_names = 'cladding_stoichiometry lanthanide_stoichiometry cladding_molar_mass cladding_density fuel_outer_radius gap_thickness thickness_variability_factor wastage_thickness_exact_pp lanthanide_flux dt'
    symbol_values = '${cladding_stoichiometry} ${lanthanide_stoichiometry} ${cladding_molar_mass} ${cladding_density} ${fuel_outer_radius} ${gap_thickness} ${thickness_variability_factor} wastage_thickness_exact_pp lanthanide_flux dt'
    expression = 'reaction_factor := (lanthanide_stoichiometry + lanthanide_stoichiometry + cladding_stoichiometry) / lanthanide_stoichiometry;
                  cladding_molar_volume := cladding_molar_mass / cladding_density;
                  geometry_factor := fuel_outer_radius / (fuel_outer_radius + gap_thickness + wastage_thickness_exact_pp);
                  velocity := reaction_factor * cladding_molar_volume * geometry_factor * thickness_variability_factor * lanthanide_flux;
                  if(velocity > 0, wastage_thickness_exact_pp + velocity * dt, wastage_thickness_exact_pp)'
  []
[]

[Materials]
  [properties]
    type = GenericFunctionMaterial
    prop_names = 'lanthanide_flux wastage_thickness_exact'
    prop_values = 'lanthanide_flux wastage_thickness_exact'
    outputs = exodus
  []
  [wastage_thickness]
    type = UPuZrLanthanideWastage
    cladding_stoichiometry = ${cladding_stoichiometry}
    lanthanide_stoichiometry = ${lanthanide_stoichiometry}
    cladding_molar_mass = ${cladding_molar_mass}
    cladding_density = ${cladding_density}
    fuel_outer_radius = ${fuel_outer_radius}
    gap_thickness = ${gap_thickness}
    thickness_variability_factor = ${thickness_variability_factor}
    lanthanide_flux = lanthanide_flux
    outputs = exodus
  []
  [value_error]
    type = ParsedMaterial
    property_name = value_error
    material_property_names = 'test:=wastage_thickness exact:=wastage_thickness_exact'
    expression = 'abs(test - exact)'
    outputs = exodus
  []
[]

[Executioner]
  type = Transient
  num_steps = 6
  dt = 1
  dtmin = 0.5
[]

[Postprocessors]
  [dt]
    type = TimestepSize
    execute_on = TIMESTEP_BEGIN
    outputs = console
  []
  [wastage_thickness_exact_pp]
    type = ElementAverageMaterialProperty
    mat_prop = wastage_thickness_exact
    execute_on = 'INITIAL TIMESTEP_END'
    outputs = console
  []
  [val_err_max]
    type = ElementExtremeMaterialProperty
    mat_prop = value_error
    value_type = max
    execute_on = TIMESTEP_END
    outputs = console
  []
[]

[Outputs]
  exodus = true
[]

(examples/metal_fuel/mechanistic_fcci/fcci.i)

# This example exercises the mechanistic Fuel-Cladding Chemical Interaction
# (FCCI) modeling approach for U-Zr and U-Pu-Zr metallic nuclear fuels. It is
# run as a SubApp, which is called by the combination of an existing assessment
# case and XXXX_multiapp.i.

# It is a collection of BISON classes and objects needed to apply a mechanistic
# FCCI model for U-Zr and U-Pu-Zr metallic nuclear fuels. It is designed to
# complement the modeling approaches adopted by the FIPD-powered X447 assessment
# cases and manually-developed X430 and IFR1 assessment cases. Thermomechanical
# behaviors are modeled in the existing assessment cases whereas lanthanide (Ln)
# transport, FCCI, and wastage growth are modeled in the SubApp. XXXX_multiapp.i
# then overrides the empirical FCCI model currently used in the assessments and
# replaces it with the mechanistic FCCI model. Examples of how to do this are
# included in the test and example specifications.

# Note that, in this model, c indicates the stable concentration of Lns. The
# model relies on an effective diffusion coefficient and flux terms informed by
# lower length scale modeling and simulations. Decay terms are included for
# illustration purposes but do not affect the solution.

# combined effective Ln production constant in mol/fission
ln_yield = 0.3 # atom/fission
avogadro = 6.0221e23 # atom/mol
production_constant = '${fparse ln_yield / avogadro}' # mol/fission

# combined effective Ln decay constant in 1/s
decay_constant = 0

# variable order, block and boundary names, and end time used in the assessment
order = placeholder
fuel_block_name = placeholder
fuel_surface_name = placeholder
end_time = placeholder

# fuel rod geometry and material properties used in the assessment
cladding_density = placeholder
fuel_outer_radius = placeholder
gap_thickness = placeholder

[GlobalParams]
  order = ${order}
  family = LAGRANGE
[]

[Problem]
  # nothing is being solved for on the cladding
  kernel_coverage_check = false
  material_coverage_check = false
[]

[Mesh]
[]

[Variables]
  [c] # stable Ln concentration in mol/m^3
    block = ${fuel_block_name}
  []
[]

[AuxVariables]
  [T]
    initial_condition = 298
  []
  [fission_rate]
    block = ${fuel_block_name}
    family = MONOMIAL
    order = CONSTANT
  []
  [porosity_aux]
    block = ${fuel_block_name}
    family = MONOMIAL
    order = CONSTANT
  []
  [sodium_logged_porosity_aux]
    block = ${fuel_block_name}
    family = MONOMIAL
    order = CONSTANT
  []
  [diffusivity]
    block = ${fuel_block_name}
    family = MONOMIAL
    order = CONSTANT
  []
  [dcdx]
    block = ${fuel_block_name}
    family = MONOMIAL
    order = CONSTANT
  []
  [c_flux]
    block = ${fuel_block_name}
    family = MONOMIAL
    order = CONSTANT
  []
[]

[AuxKernels]
  [diffusivity]
    type = MaterialRealAux
    boundary = ${fuel_surface_name}
    variable = diffusivity
    property = D
  []
  [dcdx]
    type = VariableGradientComponent
    boundary = ${fuel_surface_name}
    variable = dcdx
    gradient_variable = c
    component = x
  []
  [c_flux]
    type = ParsedAux
    boundary = ${fuel_surface_name}
    variable = c_flux
    coupled_variables = 'diffusivity dcdx'
    expression = '-diffusivity * dcdx'
  []
[]

[Kernels]
  [c_dt]
    type = TimeDerivative
    variable = c
  []
  [c_diffusion]
    type = MatDiffusion
    block = ${fuel_block_name}
    variable = c
    diffusivity = D
    args = 'c T'
  []
  [c_source]
    type = NeutronHeatSource
    block = ${fuel_block_name}
    variable = c
    fission_rate = fission_rate # fission/m^3-s
    energy_per_fission = ${production_constant} # mol/fission giving mol/m^3-s
  []
  [c_decay]
    type = Decay
    block = ${fuel_block_name}
    variable = c
    radioactive_decay_constant = ${decay_constant} # 1/s
  []
[]

[Materials]
  [porosity]
    type = ParsedMaterial
    block = ${fuel_block_name}
    property_name = porosity
    coupled_variables = porosity_aux
    expression = porosity_aux
  []
  [sodium_logged_porosity]
    type = ParsedMaterial
    block = ${fuel_block_name}
    property_name = sodium_logged_porosity
    coupled_variables = sodium_logged_porosity_aux
    expression = sodium_logged_porosity_aux
  []
  [diffusivity]
    # informed by lower length scale simulations
    type = UPuZrLanthanideDiffusivity
    block = ${fuel_block_name}
    property_name = D
    temperature = T
    porosity_name = porosity
    sodium_logged_porosity_name = sodium_logged_porosity
    outputs = exodus
    output_properties = D
  []
  [flux]
    # informed by lower length scale simulations
    type = UPuZrLanthanideFlux
    boundary = ${fuel_surface_name}
    property_name = F
    temperature = T
    concentration = c
    outputs = exodus
    output_properties = F
  []
  [wastage_thickness]
    # informed by lower length scale simulations
    type = UPuZrLanthanideWastage
    boundary = ${fuel_surface_name}
    cladding_density = ${cladding_density}
    fuel_outer_radius = ${fuel_outer_radius}
    gap_thickness =${gap_thickness}
    lanthanide_flux = F
    outputs = exodus
  []
[]

[BCs]
  [c_right]
    type = MatNeumannBC
    boundary = ${fuel_surface_name}
    variable = c
    boundary_material = F
    value = -1
  []
[]

[Executioner]
  type = Transient
  solve_type = PJFNK
  automatic_scaling = true
  compute_scaling_once = false
  petsc_options_iname = '-pc_type -pc_factor_mat_solver_package -pc_factor_shift_type -pc_factor_shift_amount'
  petsc_options_value = 'lu       superlu_dist                  NONZERO               1e-15'
  line_search = NONE
  l_max_its = 30
  l_tol = 1e-3
  nl_max_its = 30
  nl_rel_tol = 1e-10
  nl_abs_tol = 1e-6
  start_time = 0
  dt = 1e7
  end_time = ${end_time}
  verbose = true
[]

[Postprocessors]
  [c_in_fuel] # mol
    type = ElementIntegralVariablePostprocessor
    block = ${fuel_block_name}
    variable = c
    execute_on = 'initial timestep_end'
    outputs = 'console csv'
  []
  [fission_rate_total] # fission/s
    type = ElementIntegralVariablePostprocessor
    block = ${fuel_block_name}
    variable = fission_rate
    execute_on = 'initial timestep_end'
    outputs = csv
  []
  [fission_total] # fission
    type = TimeIntegratedPostprocessor
    value = fission_rate_total
    execute_on = 'initial timestep_end'
    outputs = csv
  []
  [c_produced] # mol
    type = LinearCombinationPostprocessor
    pp_names = fission_total
    pp_coefs = ${production_constant} # mol/fission giving mol
    execute_on = 'initial timestep_end'
    outputs = 'console csv'
  []
  [c_decay_rate] # mol/s
    type = LinearCombinationPostprocessor
    pp_names = c_in_fuel # mol
    pp_coefs = ${decay_constant} # 1/s
    execute_on = 'initial timestep_end'
    outputs = csv
  []
  [c_decayed] # mol
    type = TimeIntegratedPostprocessor
    value = c_decay_rate
    execute_on = 'initial timestep_end'
    outputs = csv
  []
  [c_reaction_rate] # mol/s
    type = SideDiffusiveFluxIntegral
    boundary = ${fuel_surface_name}
    variable = c
    diffusivity = D
    execute_on = 'initial timestep_end'
    outputs = csv
  []
  [c_reacted] # mol
    type = TimeIntegratedPostprocessor
    value = c_reaction_rate
    execute_on = 'initial timestep_end'
    outputs = 'console csv'
  []
  [c_flux_max]
    type = SideExtremeValue
    boundary = ${fuel_surface_name}
    variable = c_flux
    value_type = max
    execute_on = 'initial timestep_end'
    outputs = csv
  []
  [c_flux_min]
    type = SideExtremeValue
    boundary = ${fuel_surface_name}
    variable = c_flux
    value_type = min
    execute_on = 'initial timestep_end'
    outputs = csv
  []
  [wastage_thickness_max] # m
    type = ElementExtremeValue
    variable = wastage_thickness
    value_type = max
    execute_on = 'initial timestep_end'
    outputs = 'console csv'
  []
  [c_surface_max] # mol
    type = SideExtremeValue
    boundary = ${fuel_surface_name}
    variable = c
    value_type = max
    execute_on = 'initial timestep_end'
    outputs = csv
  []
  [c_surface_min] # mol
    type = SideExtremeValue
    boundary = ${fuel_surface_name}
    variable = c
    value_type = min
    execute_on = 'initial timestep_end'
    outputs = csv
  []
[]

# [VectorPostprocessors]
#   [surface_conditions]
#     type = SideValueSampler
#     variable = 'T D F c c_flux wastage_thickness'
#     boundary = ${fuel_surface_name}
#     sort_by = y
#     execute_on = 'initial timestep_end'
#     outputs = csv
#   []
# []

[Outputs]
  csv = true
  exodus = true
[]

(test/tests/upuzr_lanthanide_wastage/test.i)

cladding_stoichiometry = 18
lanthanide_stoichiometry = 3
cladding_molar_mass = 6e-2
cladding_density = 7e3
fuel_outer_radius = 2e-3
gap_thickness = 4e-4
thickness_variability_factor = 3

[Mesh]
  coord_type = RZ
  [mesh]
    type = GeneratedMeshGenerator
    dim = 1
    nx = 1
  []
[]

[Variables]
  [test]
  []
[]

[Kernels]
  [test]
    type = TimeDerivative
    variable = test
  []
[]

[Functions]
  [lanthanide_flux]
    type = ParsedFunction
    expression = '5 - t'
  []
  [wastage_thickness_exact]
    type = ParsedFunction
    symbol_names = 'cladding_stoichiometry lanthanide_stoichiometry cladding_molar_mass cladding_density fuel_outer_radius gap_thickness thickness_variability_factor wastage_thickness_exact_pp lanthanide_flux dt'
    symbol_values = '${cladding_stoichiometry} ${lanthanide_stoichiometry} ${cladding_molar_mass} ${cladding_density} ${fuel_outer_radius} ${gap_thickness} ${thickness_variability_factor} wastage_thickness_exact_pp lanthanide_flux dt'
    expression = 'reaction_factor := (lanthanide_stoichiometry + lanthanide_stoichiometry + cladding_stoichiometry) / lanthanide_stoichiometry;
                  cladding_molar_volume := cladding_molar_mass / cladding_density;
                  geometry_factor := fuel_outer_radius / (fuel_outer_radius + gap_thickness + wastage_thickness_exact_pp);
                  velocity := reaction_factor * cladding_molar_volume * geometry_factor * thickness_variability_factor * lanthanide_flux;
                  if(velocity > 0, wastage_thickness_exact_pp + velocity * dt, wastage_thickness_exact_pp)'
  []
[]

[Materials]
  [properties]
    type = GenericFunctionMaterial
    prop_names = 'lanthanide_flux wastage_thickness_exact'
    prop_values = 'lanthanide_flux wastage_thickness_exact'
    outputs = exodus
  []
  [wastage_thickness]
    type = UPuZrLanthanideWastage
    cladding_stoichiometry = ${cladding_stoichiometry}
    lanthanide_stoichiometry = ${lanthanide_stoichiometry}
    cladding_molar_mass = ${cladding_molar_mass}
    cladding_density = ${cladding_density}
    fuel_outer_radius = ${fuel_outer_radius}
    gap_thickness = ${gap_thickness}
    thickness_variability_factor = ${thickness_variability_factor}
    lanthanide_flux = lanthanide_flux
    outputs = exodus
  []
  [value_error]
    type = ParsedMaterial
    property_name = value_error
    material_property_names = 'test:=wastage_thickness exact:=wastage_thickness_exact'
    expression = 'abs(test - exact)'
    outputs = exodus
  []
[]

[Executioner]
  type = Transient
  num_steps = 6
  dt = 1
  dtmin = 0.5
[]

[Postprocessors]
  [dt]
    type = TimestepSize
    execute_on = TIMESTEP_BEGIN
    outputs = console
  []
  [wastage_thickness_exact_pp]
    type = ElementAverageMaterialProperty
    mat_prop = wastage_thickness_exact
    execute_on = 'INITIAL TIMESTEP_END'
    outputs = console
  []
  [val_err_max]
    type = ElementExtremeMaterialProperty
    mat_prop = value_error
    value_type = max
    execute_on = TIMESTEP_END
    outputs = console
  []
[]

[Outputs]
  exodus = true
[]

Description
FCCI Modeling Example
Example Input Syntax
Input Parameters
Input Files
References