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:

$var element = document.getElementById("moose-equation-925636b6-f16b-4d00-95b8-547eab1533bc");katex.render("-D_0 \\frac{\\partial c_0}{\\partial x} = -D_1 \\frac{\\partial c_1}{\\partial x}", element, {displayMode:true,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$

where $var element = document.getElementById("moose-equation-6bc57d22-7334-4f40-a58f-55edba5f7de8");katex.render("D_i", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ is the diffusion coefficient of specie $var element = document.getElementById("moose-equation-72e90152-ba45-4dc8-8507-46f2e1994e86");katex.render("i", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ in subdomain $var element = document.getElementById("moose-equation-c1ed5161-273c-4c51-bfa1-02a4f37f2022");katex.render("i", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ , and $var element = document.getElementById("moose-equation-98886ad2-59e2-48b1-83e0-4c8621b2ac10");katex.render("c_i", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ is the concentration of specie $var element = document.getElementById("moose-equation-762ef062-0754-430b-9bae-c51246cf9181");katex.render("i", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ in subdomain $var element = document.getElementById("moose-equation-3d54fba0-b6fa-4d58-b0f5-c65a7dbf7abd");katex.render("i", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ . An example of this condition is shown in the MOOSE test directory; see files below:

(modules/doc/2d_interface/coupled_value_coupled_flux.i)

(../../InterfaceDiffusion.C)

(../../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 $var element = document.getElementById("moose-equation-1f6a02cd-35da-4d68-a142-5e6d22f620b7");katex.render("c_0", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ from our example above.
neighbor_var: The "secondary" variable. This could be $var element = document.getElementById("moose-equation-ee537a0b-ebb0-47a4-946e-da4040aa9596");katex.render("c_1", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ 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.

Available Objects

Moose App
InterfaceReactionImplements a reaction to establish ReactionRate=k_f*u-k_b*v at interface.
Heat Conduction App
ConjugateHeatTransferThis InterfaceKernel models conjugate heat transfer. Fluid side must be primary side and solid side must be secondary side. T_fluid is provided in case that variable ( fluid energy variable) is not temperature but e.g. internal energy.
SideSetHeatTransferKernelModeling conduction, convection, and radiation across internal side set.
Fsi App
CoupledPenaltyInterfaceDiffusionEnforces continuity of flux and continuity of solution via penalty across an interface.
StructureAcousticInterfaceEnforces displacement and stress/pressure continuity between the fluid and structural domains. Element is always the structure and neighbor is always the fluid.
Tensor Mechanics App
CZMInterfaceKernelInterface kernel for use with cohesive zone models (CZMs) that compute traction as a function of the displacement jump
Phase Field App
EqualGradientLagrangeInterfaceEnforce componentwise gradient continuity between two different variables across a subdomain boundary using a Lagrange multiplier
EqualGradientLagrangeMultiplierLagrange multiplier kernel for EqualGradientLagrangeInterface.
InterfaceDiffusionBoundaryTermAdd weak form surface terms of the Diffusion equation for two different variables across a subdomain boundary
InterfaceDiffusionFluxMatchEnforce flux continuity between two different variables across a subdomain boundary

Available Actions

Moose App
AddInterfaceKernelActionAdd an InterfaceKernel object to the simulation.

(modules/doc/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
[]

(../../InterfaceDiffusion.C)

// This file is part of the MOOSE framework
// https://www.mooseframework.org
//
// 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("MooseTestApp", 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.");
  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;
}

(../../InterfaceDiffusion.h)

// This file is part of the MOOSE framework
// https://www.mooseframework.org
//
// 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;
};

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