CoupledVarThresholdElementSubdomainModifier

Overview

The CoupledVarThresholdElementSubdomainModifier can model

• Element death (with applications in ablation, fracture, etc.);

• Element activation (with applications in additive manufacturing, sintering, solidification, etc.);

• Moving interface (with applications in metal oxidation, phase transformation, melt pool, etc.).

The CoupledVarThresholdElementSubdomainModifier changes the element subdomain based on the given criterion. It also handles the corresponding

• Moving boundary/interface nodeset/sideset modification,

• Solution initialization, and

• Stateful material property initialization,

all of which are demonstrated using the following example.

Consider a unit square domain, and an auxiliary variable defined by the function . The function represents a signed-distance function of a circle of radius whose center is moving along the x-axis towards right.

Initially, the domain is decomposed by a vertical line . The elements on the left side of the vertical line have subdomain ID of 1, and the elements on the right side have subdomain ID of 2. The CoupledVarThresholdElementSubdomainModifier is used to change the subdomain ID from 2 to 1 for elements within the circle.

Reversible vs. irreversible modification

If the CoupledVarThresholdElementSubdomainModifier is applied onto the entire domain, and the parameter complement_subdomain_id is set to 2, then the subdomain ID of all elements outside the circle will be set to 2:

  [moving_circle]
    type = CoupledVarThresholdElementSubdomainModifier
    coupled_var = 'phi'
    criterion_type = BELOW
    threshold = 0
    subdomain_id = 1
    complement_subdomain_id = 2
    moving_boundary_name = moving_boundary
    execute_on = 'INITIAL TIMESTEP_BEGIN'
  []

The result of a reversible element subdomain modifier at three different time steps

However, in many applications, e.g. element death and activation, the equivalent movement of element subdomains is not reversible. In this case, omitting the parameter complement_subdomain_id will make the subdomain modification irreversible:

  [moving_circle]
    type = CoupledVarThresholdElementSubdomainModifier
    coupled_var = 'phi'
    block = 2
    criterion_type = BELOW
    threshold = 0
    subdomain_id = 1
    moving_boundary_name = moving_boundary
    execute_on = 'INITIAL TIMESTEP_BEGIN'
  []

The result of an irreversible element subdomain modifier at three different time steps

Moving boundary/interface nodeset/sideset modification

The change of element subdomains will alter the definition of certain sidesets and nodesets. The CoupledVarThresholdElementSubdomainModifier optionally takes the parameter moving_boundary_name to help modify the corresponding sideset/nodeset. If the boundary provided through the moving_boundary_name parameter already exists, the modifier will attempt to modify the provided sideset/nodeset whenever an element changes subdomain. If the boundary does not exist, the modifier will create a sideset and a nodeset with the provided name.

The evolving sideset (green) at three different time steps

The evolving nodeset (green) at three different time steps

Nodal and integrated BCs can be applied on the moving boundary.

Solution initialization

Depending on the physics, one may or may not want to initialize the solution when an element and its related nodes change subdomain. The parameter apply_initial_conditions defaults to true and determines whether the initial conditions should be re-evaluated.

Suppose initially there is an auxiliary variable everywhere inside the domain, and the variable value in subdomain 1 (blue) doubles at each time step:

[AuxVariables]
  [u]
    [InitialCondition]
      type = ConstantIC
      value = 1
    []
  []
  [phi]
  []
[]

[AuxKernels]
  [phi]
    type = FunctionAux
    variable = phi
    function = moving_circle
    execute_on = 'INITIAL TIMESTEP_BEGIN TIMESTEP_END'
  []
  [double_u]
    type = StatefulAux
    variable = u
    coupled = u
    block = 1
  []
[]

The auxiliary variable at three different time steps

Stateful material property initialization

Similarly, all stateful material properties will be re-initialized when an element changes subdomain. Suppose initially the diffusivity is everywhere, and the diffusivity doubles at each time step:

[Materials]
  [stateful]
    type = StatefulMaterial
    initial_diffusivity = 0.5
    multiplier = 2
    block = 1
    outputs = exodus
  []
  [non_stateful]
    type = GenericConstantMaterial
    prop_names = 'diffusivity'
    prop_values = '0.5'
    block = 2
    outputs = exodus
  []
[]

The diffusivity at three different time steps

Input Parameters

Input Files

• (test/tests/userobjects/element_subdomain_modifier/initial_condition.i)
• (test/tests/userobjects/element_subdomain_modifier/no_moving_boundary.i)
• (test/tests/userobjects/element_subdomain_modifier/block_restricted.i)
• (test/tests/userobjects/element_subdomain_modifier/steady.i)
• (test/tests/userobjects/element_subdomain_modifier/reversible.i)
• (test/tests/userobjects/element_subdomain_modifier/stateful_property.i)