InterfaceKernels System

Interface kernels are meant to assist in coupling different physics across sub-domains. The most straightforward example is the case in which one wants to set the flux of a specie A in subdomain 0 equal to the flux of a specie B in subdomain 1 at the boundary between subdomains 0 and 1. In mathematical terms, we might be interested in establishing the condition:

$var element = document.getElementById("moose-equation-1af9c775-6208-4391-ba27-7cfd28201513");katex.render("-D_0 \\frac{\\partial c_0}{\\partial x} = -D_1 \\frac{\\partial c_1}{\\partial x}", element, {displayMode:true,throwOnError:false});$

where $var element = document.getElementById("moose-equation-ea48629c-7511-4c31-961f-ea18b25f2020");katex.render("D_i", element, {displayMode:false,throwOnError:false});$ is the diffusion coefficient of specie $var element = document.getElementById("moose-equation-6234aa8f-aa6d-4b7e-a056-2ceb683957cd");katex.render("i", element, {displayMode:false,throwOnError:false});$ in subdomain $var element = document.getElementById("moose-equation-9bdc0a48-d192-4b5e-a8af-42e49be670dc");katex.render("i", element, {displayMode:false,throwOnError:false});$ , and $var element = document.getElementById("moose-equation-77f122f8-adac-4a94-81b6-28e7162fb414");katex.render("c_i", element, {displayMode:false,throwOnError:false});$ is the concentration of specie $var element = document.getElementById("moose-equation-f179fbcc-a545-4ad9-bc53-e20c8f1efd67");katex.render("i", element, {displayMode:false,throwOnError:false});$ in subdomain $var element = document.getElementById("moose-equation-b396427a-1b9f-48b8-b4da-4e6c99e64961");katex.render("i", element, {displayMode:false,throwOnError:false});$ . An example of this condition is shown in the MOOSE test directory; see files below:

(moose/test/tests/interfacekernels/2d_interface/coupled_value_coupled_flux.i)

(moose/framework/src/interfacekernels/InterfaceDiffusion.C)

(moose/framework/include/interfacekernels/InterfaceDiffusion.h)

Interface kernels can be used to provide any general flux condition at an interface, and even more generally can be used to impose any interfacial condition that requires access to values of different variables and gradients of different variables on either side of an interface. In an input file, the user will specify at a minimum the following parameters:

type: The type of interface kernel to be used
variable: This is the "primary" variable. Note that the primary variable must exist on the same subdomain as the sideset specified in the boundary parameter. The existence of a "primary" and "secondary" or "neighbor" variable ensures that the interface kernel residual and jacobian functions get called the correct number of times. variable could be $var element = document.getElementById("moose-equation-c68a040e-b895-4528-8c1b-91988e133ee3");katex.render("c_0", element, {displayMode:false,throwOnError:false});$ from our example above.
neighbor_var: The "secondary" variable. This could be $var element = document.getElementById("moose-equation-604ba0f2-346e-4b2c-8b5e-4d76bc835040");katex.render("c_1", element, {displayMode:false,throwOnError:false});$ from our example above.
boundary: The interfacial boundary between the subdomains. Note that this must be a sideset and again must exist on the same subdomain as the primary variable. The fact that this boundary is a sideset allows access to variable gradients.

For additional information about the interface kernel system, don't hesitate to contact the MOOSE Discussion forum.

Multiple system support

Using multiple nonlinear system with interface kernels is currently not supported. The only feature supported, which can at times suffice, notably when using MultiApps to couple equations, is to use an auxiliary variable as the neighbor_var.

Available Objects

Moose App
ADMatInterfaceReactionImplements a reaction to establish ReactionRate=k_f*u-k_b*v at interface.
ADPenaltyInterfaceDiffusionA penalty-based interface condition that forcesthe continuity of variables and the flux equivalence across an interface.
ADVectorPenaltyInterfaceDiffusionA penalty-based interface condition that forcesthe continuity of variables and the flux equivalence across an interface.
InterfaceDiffusionThe kernel is utilized to establish flux equivalence on an interface for variables.
InterfaceReactionImplements a reaction to establish ReactionRate=k_f*u-k_b*v at interface.
PenaltyInterfaceDiffusionA penalty-based interface condition that forcesthe continuity of variables and the flux equivalence across an interface.
VectorPenaltyInterfaceDiffusionA penalty-based interface condition that forcesthe continuity of variables and the flux equivalence across an interface.
Electromagnetics App
ElectrostaticContactConditionInterface condition that describes the current continuity and contact conductance across a boundary formed between two dissimilar materials (resulting in a potential discontinuity). Conductivity on each side of the boundary is defined via the material properties system.
ParallelElectricFieldInterfaceVectorInterfaceKernel that implements the condition $var element = document.getElementById("moose-equation-fe2ca2cb-bc89-4ce4-923e-45fdfdc3566c");katex.render("\\vec{E}_{1}^{\\parallel} - \\vec{E}_{2}^{\\parallel} = 0", element, {displayMode:false,throwOnError:false});$
PerpendicularElectricFieldInterfaceVectorInterfaceKernel that implements the condition $var element = document.getElementById("moose-equation-78a1ae53-35cc-4b62-92d1-22100d4171fd");katex.render("\\epsilon_1 \\vec{E}_{1}^{\\perp} - \\epsilon_2 \\vec{E}_{2}^{\\perp} = \\sigma_f", element, {displayMode:false,throwOnError:false});$
Zapdos App
HphiRadialInterfaceUsed to include the electric field into or out of a neighboring subdomain. This is done using Ampère–Maxwell law to relate the azmithal magnetic flux to the axial electric field.
InterfaceAdvectionUsed to include the electric field driven advective flux of a species into or out of a neighboring subdomain.
InterfaceLogDiffusionElectronsUsed to include the diffusive flux of species into or out of a neighboringsubdomain. Currently specific to electrons.
PotentialSurfaceCharge
Squirrel App
InterTemperatureAdvectionDG upwinding for the convection

Available Actions

Moose App
AddInterfaceKernelActionAdd an InterfaceKernel object to the simulation.

(moose/test/tests/interfacekernels/2d_interface/coupled_value_coupled_flux.i)

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 2
    xmax = 2
    ny = 2
    ymax = 2
  []
  [./subdomain1]
    input = gen
    type = SubdomainBoundingBoxGenerator
    bottom_left = '0 0 0'
    top_right = '1 1 0'
    block_id = 1
  [../]
  [./interface]
    type = SideSetsBetweenSubdomainsGenerator
    input = subdomain1
    primary_block = '0'
    paired_block = '1'
    new_boundary = 'primary0_interface'
  [../]
  [./break_boundary]
    input = interface
    type = BreakBoundaryOnSubdomainGenerator
  [../]
[]

[Variables]
  [./u]
    order = FIRST
    family = LAGRANGE
    block = 0
  [../]

  [./v]
    order = FIRST
    family = LAGRANGE
    block = 1
  [../]
[]

[Kernels]
  [./diff_u]
    type = CoeffParamDiffusion
    variable = u
    D = 4
    block = 0
  [../]
  [./diff_v]
    type = CoeffParamDiffusion
    variable = v
    D = 2
    block = 1
  [../]
  [./source_u]
    type = BodyForce
    variable = u
    value = 1
  [../]
[]

[InterfaceKernels]
  [./interface]
    type = PenaltyInterfaceDiffusion
    variable = u
    neighbor_var = v
    boundary = primary0_interface
    penalty = 1e6
  [../]
[]

[BCs]
  [./u]
    type = VacuumBC
    variable = u
    boundary = 'left_to_0 bottom_to_0 right top'
  [../]
  [./v]
    type = VacuumBC
    variable = v
    boundary = 'left_to_1 bottom_to_1'
  [../]
[]

[Postprocessors]
  [./u_int]
    type = ElementIntegralVariablePostprocessor
    variable = u
    block = 0
  [../]
  [./v_int]
    type = ElementIntegralVariablePostprocessor
    variable = v
    block = 1
  [../]
[]

[Preconditioning]
  [./smp]
    type = SMP
    full = true
  [../]
[]

[Executioner]
  type = Steady
  solve_type = NEWTON
[]

[Outputs]
  exodus = true
  print_linear_residuals = true
[]

(moose/framework/src/interfacekernels/InterfaceDiffusion.C)

// This file is part of the MOOSE framework
// https://mooseframework.inl.gov
//
// All rights reserved, see COPYRIGHT for full restrictions
// https://github.com/idaholab/moose/blob/master/COPYRIGHT
//
// Licensed under LGPL 2.1, please see LICENSE for details
// https://www.gnu.org/licenses/lgpl-2.1.html

#include "InterfaceDiffusion.h"

registerMooseObject("MooseApp", InterfaceDiffusion);

InputParameters
InterfaceDiffusion::validParams()
{
  InputParameters params = InterfaceKernel::validParams();
  params.addParam<MaterialPropertyName>("D", "D", "The diffusion coefficient.");
  params.addParam<MaterialPropertyName>(
      "D_neighbor", "D_neighbor", "The neighboring diffusion coefficient.");
  params.addClassDescription(
      "The kernel is utilized to establish flux equivalence on an interface for variables.");
  return params;
}

InterfaceDiffusion::InterfaceDiffusion(const InputParameters & parameters)
  : InterfaceKernel(parameters),
    _D(getMaterialProperty<Real>("D")),
    _D_neighbor(getNeighborMaterialProperty<Real>("D_neighbor"))
{
}

Real
InterfaceDiffusion::computeQpResidual(Moose::DGResidualType type)
{
  Real r = 0;

  switch (type)
  {
    case Moose::Element:
      r = _test[_i][_qp] * -_D_neighbor[_qp] * _grad_neighbor_value[_qp] * _normals[_qp];
      break;

    case Moose::Neighbor:
      r = _test_neighbor[_i][_qp] * _D[_qp] * _grad_u[_qp] * _normals[_qp];
      break;
  }

  return r;
}

Real
InterfaceDiffusion::computeQpJacobian(Moose::DGJacobianType type)
{
  Real jac = 0;

  switch (type)
  {
    case Moose::ElementElement:
    case Moose::NeighborNeighbor:
      break;

    case Moose::NeighborElement:
      jac = _test_neighbor[_i][_qp] * _D[_qp] * _grad_phi[_j][_qp] * _normals[_qp];
      break;

    case Moose::ElementNeighbor:
      jac = _test[_i][_qp] * -_D_neighbor[_qp] * _grad_phi_neighbor[_j][_qp] * _normals[_qp];
      break;
  }

  return jac;
}

(moose/framework/include/interfacekernels/InterfaceDiffusion.h)

// This file is part of the MOOSE framework
// https://mooseframework.inl.gov
//
// All rights reserved, see COPYRIGHT for full restrictions
// https://github.com/idaholab/moose/blob/master/COPYRIGHT
//
// Licensed under LGPL 2.1, please see LICENSE for details
// https://www.gnu.org/licenses/lgpl-2.1.html

#pragma once

#include "InterfaceKernel.h"

/**
 * DG kernel for interfacing diffusion between two variables on adjacent blocks
 */
class InterfaceDiffusion : public InterfaceKernel
{
public:
  static InputParameters validParams();

  InterfaceDiffusion(const InputParameters & parameters);

protected:
  virtual Real computeQpResidual(Moose::DGResidualType type) override;
  virtual Real computeQpJacobian(Moose::DGJacobianType type) override;

  const MaterialProperty<Real> & _D;
  const MaterialProperty<Real> & _D_neighbor;
};

Multiple system support
Available Objects
Available Actions