LinearFVKernels System

For the finite volume method (FVM) when used without Newton's method, LinearFVKernel is the base class for LinearFVFluxKernel and LinearFVElementalKernel. These specialized objects satisfy the following tasks:

* LinearFVFluxKernel adds contributions to system matrices and right hand sides coming from flux terms over the faces between cells and boundaries. Diffusion and advection terms in PDEs serve as good examples for these kernels.

* LinearFVElementalKernel adds contributions to system matrices and right hand sides from volumetric integrals. Volumetric source terms or reaction terms serve as good examples for these kernels.

For more information on general design choices in this setting click here

LinearFVKernels block

FVM kernels which contribute to systems that are not solved via Newton's method are added to simulation input files in the LinearFVKernels block. The LinearFVKernels block in the example below sets up a steady-state diffusion problem defined by the equation:

The diffusion term is represented by the kernel named diffusion.

Example of the LinearFVKernels block in a MOOSE input file.

[LinearFVKernels]
  [diffusion]
    type = LinearFVDiffusion
    variable = u
    diffusion_coeff = coeff_func
    use_nonorthogonal_correction = false
  []
  [source]
    type = LinearFVSource
    variable = u
    source_density = source_func
  []
[]
(moose/test/tests/linearfvkernels/diffusion/diffusion-2d.i)

The LinearFVSource in the example derives from LinearFVElementalKernel so it's a volumetric contribution to the right hand side, while the LinearFVDiffusion is an LinearFVFluxKernel and it's a face contribution to the system matrix and right hand side. The remaining MOOSE syntax is what you would expect to see in finite element kernel objects. The variable parameter refers to the variable that this kernel is acting on (i.e. into which equation do the contributions of this term go). This must be a linear finite-volume variable in this case.

Boundary conditions are not discussed in these examples. We recommend visiting the [LinearFVBCs/index.md) page for details about boundary conditions.

Available Objects

  • Moose App
  • LinearFVAdvectionRepresents the matrix and right hand side contributions of an advection term in a partial differential equation.
  • LinearFVAnisotropicDiffusionRepresents the matrix and right hand side contributions of a diffusion term in a partial differential equation.
  • LinearFVDiffusionRepresents the matrix and right hand side contributions of a diffusion term in a partial differential equation.
  • LinearFVReactionRepresents the matrix and right hand side contributions of a reaction term () in a partial differential equation.
  • LinearFVSourceRepresents the matrix and right hand side contributions of a solution-independent source term in a partial differential equation.
  • LinearFVTimeDerivativeRepresents the matrix and right hand side contributions of a time derivative term in a partial differential equation.