Penalty Dirichlet Old Value Nodal Kernel

Description

The PenaltyDirichletOldValuePD NodalKernel is used to apply Dirichlet boundary conditions with value of old variable solution using the penalty method for nodesets. It is similar to imposing Dirichlet boundary condition using penalty method, but implemented using nodal kernel.

Example Syntax

#In order to compare the solution generated using preset Dirichlet BC, the penalty was set to 1e10.
#Large penalty number should be used with caution.

[Mesh<<<{"href": "../../syntax/Mesh/index.html"}>>>]
  type = PeridynamicsMesh
  horizon_number = 3

  [./gfm]
    type = GeneratedMeshGenerator<<<{"description": "Create a line, square, or cube mesh with uniformly spaced or biased elements.", "href": "../meshgenerators/GeneratedMeshGenerator.html"}>>>
    dim<<<{"description": "The dimension of the mesh to be generated"}>>> = 2
    xmin<<<{"description": "Lower X Coordinate of the generated mesh"}>>> = -1.1
    xmax<<<{"description": "Upper X Coordinate of the generated mesh"}>>> = 1.1
    ymin<<<{"description": "Lower Y Coordinate of the generated mesh"}>>> = -1.1
    ymax<<<{"description": "Upper Y Coordinate of the generated mesh"}>>> = 1.1
    nx<<<{"description": "Number of elements in the X direction"}>>> = 11
    ny<<<{"description": "Number of elements in the Y direction"}>>> = 11
    elem_type<<<{"description": "The type of element from libMesh to generate (default: linear element for requested dimension)"}>>> = QUAD4
  [../]
  [./gpd]
    type = MeshGeneratorPD<<<{"description": "Mesh generator class to convert FE mesh to PD mesh", "href": "../meshgenerators/MeshGeneratorPD.html"}>>>
    input<<<{"description": "The mesh based on which PD mesh will be created"}>>> = gfm
    retain_fe_mesh<<<{"description": "Whether to retain the FE mesh or not after conversion into PD mesh"}>>> = false
  [../]
[]

[Variables<<<{"href": "../../syntax/Variables/index.html"}>>>]
  [./temp]
  [../]
[]

[AuxVariables<<<{"href": "../../syntax/AuxVariables/index.html"}>>>]
  [./bond_status]
    initial_condition<<<{"description": "Specifies a constant initial condition for this variable"}>>> = 1
  [../]
[]

[Kernels<<<{"href": "../../syntax/Kernels/index.html"}>>>]
  [./heat]
    type = HeatConductionBPD<<<{"description": "Class for calculating the residual and Jacobian for the bond-based peridynamic heat conduction formulation", "href": "../kernels/HeatConductionBPD.html"}>>>
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = temp
  [../]
  [./source]
    type = HeatSourceBPD<<<{"description": "Class for calculating the residual from heat source for the bond-based peridynamic heat conduction formulation", "href": "../kernels/HeatSourceBPD.html"}>>>
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = temp
    power_density<<<{"description": "Volumetric heat source density"}>>> = '-4'
  [../]
[]

[Materials<<<{"href": "../../syntax/Materials/index.html"}>>>]
  [./thermal_material]
    type = ThermalConstantHorizonMaterialBPD<<<{"description": "Class for computing peridynamic micro conductivity for bond-based model using regular uniform mesh", "href": "../materials/ThermalConstantHorizonMaterialBPD.html"}>>>
    thermal_conductivity<<<{"description": "Name of material property defining thermal conductivity"}>>> = 1
    temperature<<<{"description": "Nonlinear variable name for the temperature"}>>> = temp
  [../]
[]

[NodalKernels<<<{"href": "../../syntax/NodalKernels/index.html"}>>>]
  [./bc_all]
    type = PenaltyDirichletOldValuePD<<<{"description": "Enforces a Dirichlet boundary condition in a weak sense by penalizing differences between the current solution and the old solution for transient problems.", "href": "PenaltyDirichletOldValuePD.html"}>>>
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = temp
    boundary<<<{"description": "The list of boundaries (ids or names) from the mesh where this object applies"}>>> = 'pd_nodes_top pd_nodes_left pd_nodes_right pd_nodes_bottom'
    penalty<<<{"description": "Penalty scalar"}>>> = 1e10
  [../]
[]

# [BCs]
#   [./fix]
#     type = DirichletBC
#     variable = temp
#     value = 0
#     boundary = 'pd_nodes_top pd_nodes_left pd_nodes_right pd_nodes_bottom'
#   [../]
# []

[Executioner<<<{"href": "../../syntax/Executioner/index.html"}>>>]
  type = Transient
  solve_type = 'PJFNK'

  start_time = 0
  end_time = 1
  nl_rel_tol = 1e-14
[]

[Outputs<<<{"href": "../../syntax/Outputs/index.html"}>>>]
  file_base<<<{"description": "Common file base name to be utilized with all output objects"}>>> = preset_bc_out
  exodus<<<{"description": "Output the results using the default settings for Exodus output."}>>> = true
[]

Input Parameters

Input Files

• (modules/peridynamics/test/tests/nodalkernels/penalty_dirichlet_old_value.i)