BCs

Achlys Boundary Conditions

New boundary conditions available through the Achlys app are listed below. These mostly implement some form of recombination flux of the form given in Eq. (1).

$(1)var element = document.getElementById("moose-equation-ea31ee04-443a-4742-9f78-fc8dd819f9d6");katex.render(" \\varphi_{out} = K_{r}C_{m}^2", element, {displayMode:true,throwOnError:false});$

Where the recombination coefficient, $var element = document.getElementById("moose-equation-7ce383f3-2501-4b0d-8a89-32ebaf29df57");katex.render("K_r", element, {displayMode:false,throwOnError:false});$ , is given by Eq. (2).

$(2)var element = document.getElementById("moose-equation-2594e2d3-f22d-42b8-8396-f054e398ddbf");katex.render(" K_{r}(T) = K_0\\exp\\left(-E_r / k_B T\\right)", element, {displayMode:true,throwOnError:false});$

Available BCs

achlys App
ADSurfaceRecombinationImposes the integrated boundary condition $var element = document.getElementById("moose-equation-e72bfc3a-c4ad-4210-8dc2-97c5672c8442");katex.render("\\frac{\\partial u}{\\partial n}= kv^2", element, {displayMode:false,throwOnError:false});$ , where $var element = document.getElementById("moose-equation-cd89c800-8c5d-4761-aec7-514a69028aa0");katex.render("v", element, {displayMode:false,throwOnError:false});$ is a variable and the constant, k, is calculated from an Arhhenious expression based on provided (constant) values of E and T
ADSurfaceRecombinationCoupledTImposes the integrated boundary condition $var element = document.getElementById("moose-equation-36a3e44b-f563-4694-aa88-23d7230869fb");katex.render("\\frac{\\partial u}{\\partial n}= kv^2", element, {displayMode:false,throwOnError:false});$ , where $var element = document.getElementById("moose-equation-9fd58896-87bf-4908-8b88-c0283b05e172");katex.render("v", element, {displayMode:false,throwOnError:false});$ is a variable and the constant, k, is calculated from an Arhhenious expression based on an energy barrier, E, and a coupled Temperature.
DirichletEquivalentPfcImplantBCImposes the essential boundary condition $var element = document.getElementById("moose-equation-3a1ed50f-46d2-4813-9dce-af8b9f3ddb38");katex.render("u=g", element, {displayMode:false,throwOnError:false});$ , where $var element = document.getElementById("moose-equation-90fc976f-103b-4dab-b87b-92c69ac391af");katex.render("g", element, {displayMode:false,throwOnError:false});$ is a constant calculated assuming the recombination fluxquickly becomes equal to the incident flux. The recombination term is calculated using the simulation temperature and the pre-exponent and Energy values provided
DirichletPfcFunctionFluxRampBCImposes the essential boundary condition $var element = document.getElementById("moose-equation-385b4dc2-08ee-4b30-9212-514d86e8f96f");katex.render("u=g", element, {displayMode:false,throwOnError:false});$ , where $var element = document.getElementById("moose-equation-9dfcd84b-e2d3-475c-a045-3306205e5a81");katex.render("g", element, {displayMode:false,throwOnError:false});$ is a constant calculated assuming the recombination fluxquickly becomes equal to the incident flux. The recombination term is calculated using the simulation temperature and the pre-exponent and Energy values provided
PfcFunctionFluxRampBCImposes the essential boundary condition $var element = document.getElementById("moose-equation-949a4494-b361-4b4e-9aac-ce5e8258ca56");katex.render("u=g", element, {displayMode:false,throwOnError:false});$ , where $var element = document.getElementById("moose-equation-fcfccc2e-b270-46e8-a9af-f486b4f9d1b7");katex.render("g", element, {displayMode:false,throwOnError:false});$ is a constant calculated assuming the recombination fluxquickly becomes equal to the incident flux. The recombination term is calculated using the simulation temperature and the pre-exponent and Energy values provided

Common Framework BCs

See below for framework documentation on commonly used boundary conditions that are not specific to the Achlys module. Note the full list of MOOSE BCs can be found here

Name	Description	Link
Dirichlet	Constant value	ADDirichletBC
Neumann	Constant gradient	ADNeumannBC

Heat Transfer BCs

As is the case for all Thermal transport considerations within Achlys, all MOOSE objects are taken directly from either the framework or Heat Conduction App

See the example below for applying thermal boundary conditions to a material where:

A constant heat flux of $var element = document.getElementById("moose-equation-4de06401-fd26-4bc4-9e80-18c450357314");katex.render("10 \\text{\\:MW\\:m}^{-2}", element, {displayMode:false,throwOnError:false});$ is applied tot the top surface
A convective heat flux is applied to another surface with some specified heat flux coefficiant

[BCs]
  [./pfc_t]
    type = ADNeumannBC
    variable = Temperature
    boundary = 2
    value = 1.00e+7 # W/m2
  [../]
  [./cooling_t]
    type = ADConvectiveHeatFluxBC
    variable = Temperature
    boundary = 5
    T_infinity = 323
    heat_transfer_coefficient = 70000
  [../]
[]

(test/tests/kernels/steady_heat_transfer/temperature.i)

[Mesh]
  [./unlabelled]
    file = monoblock.msh
    type = FileMeshGenerator
    construct_side_list_from_node_list=true
  [../] 
  [./block_1]
    type= AllSideSetsByNormalsGenerator
    input = unlabelled
    fixed_normal = false
  [../]
[]

[Problem]
  type = FEProblem # This is the "normal" type of Finite Element Problem in MOOSE
  coord_type = XYZ # cartesian
[]

[Variables]
  [./Temperature]
    initial_condition = 323
  [../]
[]

[Kernels]
  [./Temperature_evolution]
    variable = Temperature
    type = ADHeatConduction
    thermal_conductivity = conductivity
  [../]
[]
[BCs]
  [./pfc_t]
    type = ADNeumannBC 
    variable = Temperature
    boundary = 2
    value = 1.00e+7 # W/m2
  [../]
  [./cooling_t]
    type = ADConvectiveHeatFluxBC
    variable = Temperature
    boundary = 5
    T_infinity = 323
    heat_transfer_coefficient = 70000
  [../]
[]

[Materials]
   [./W]
    type = TrappingMaterial
    v1 = 1.0E13
    v2 = 1.0E13
    v3 = 1.0E13
    E1 = 0.86
    E2 = 1.0
    E3 = 0.0
    k_boltz = 8.6E-5
    D0 = 4.1E-7
    E_diff = 0.39
    lambda = 1.1E-10
    n_sol = 6
    n1 = 1E-3 #1.0E25
    n2 = 4e-4
    n3 = 0.0
    Temperature = Temperature
    block = 'W'
# thermal properties
    conductivity = 150 # W/K
    Cp = 137 # J/(kg K)
    density = 19300 # kg/m3
  [../]
  [./Cu]
    type = TrappingMaterial
    v1 = 1.0E13
    v2 = 1.0E13
    v3 = 1.0E13
    E1 = 0.0
    E2 = 0.0
    E3 = 0.0
    k_boltz = 8.6E-5
    D0 = 3.5E-5
    E_diff = 0.67
    lambda = 1.1E-10
    n_sol = 6
    n1 = 0.0 #1.0E25
    n2 = 0.0
    n3 = 0.0
    Temperature = Temperature
    block = 'Cu'
# thermal properties
    conductivity = 350 # W/K
    Cp = 380 # J/(kg K)
    density = 8900 # kg/m3
  [../]
  [./CuCrZr]
    type = TrappingMaterial
    v1 = 1.0E13
    v2 = 1.0E13
    v3 = 1.0E13
    E1 = 0.0
    E2 = 0.0
    E3 = 0.5
    k_boltz = 8.6E-5
    D0 = 6.6E-7
    E_diff = 1.00
    lambda = 1.1E-10
    n_sol = 6
    n1 = 0.0
    n2 = 0.0
    n3 = 5.87e-5
    Temperature = Temperature
    block = 'CuCrZr'
# thermal properties
    conductivity = 300  # W/K
    Cp = 400 # J/(kg K)
    density = 8960 # kg/m3
  [../]
[]

[Executioner]
  type = Steady
  solve_type = NEWTON
  automatic_scaling = true
  # compute_scaling_once = false
  # l_tol = 1e-10
  # nl_rel_tol = 1e-7
  #resid_vs_jac_scaling_param = 0.5
  petsc_options_iname = '-ksp_type -pc_type -snes_type'
  petsc_options_value = 'bcgs lu fas'
[]
[Preconditioning]
  [./smp]
    type = SMP
    full = true
  [../]
[]
[Outputs]
  exodus = true # Output Exodus format
  csv = true
[]
[Debug]
  show_material_props = true
  show_var_residual_norms = true
[]

[Postprocessors]
  [/pfc_flux]
    type = ADSideFluxIntegral
    variable = Temperature
    boundary = 2
    diffusivity = conductivity #thermal_diffusivity #conductivity
  [../]
  [cooling_surface_flux]
    type = ADSideFluxIntegral
    variable = Temperature
    boundary = 5
    diffusivity = conductivity
  [../]
  [./max_ab]
    type = SideMaxValue
    v = Temperature
    start_point = '0.015 0.029 0'
    end_point = '0.015 0.0205 0'
  [../]
  [./min_ab]
    type = SideMinValue
    v = Temperature
    start_point = '0.015 0.029 0'
    end_point = '0.015 0.0205 0'
  [../]
[]

Achlys Boundary Conditions
Available BCs
Common Framework BCs
Heat Transfer BCs

Module

Examples

Source Code

Comparison to Analytical Solution

Thermal Desorption Spectrum

Kernels

BCs

Materials

Postprocessors

BCs

Achlys Boundary Conditions

Available BCs

Common Framework BCs

Heat Transfer BCs