MooseVariableFVReal

Overview

The MooseVariableFV template supports creation of finite volume variable types. At the time of writing there is only one used instantiation of the template which is MooseVariableFVReal. MOOSE uses cell-centered finite volumes which can be conveniently supported by the CONSTANT MONOMIAL finite element type in the background.

One important parameter for MooseVariableFV objects is two_term_boundary_expansion. By default this is false. When false, boundary faces which do not have associated Dirichlet boundary conditions simply use the cell centroid value as the face value. However, when two_term_boundary_expansion is set to true in the Variables sub-block of the finite volume variable, then the cell centroid value and the reconstructed cell centroid gradient (hence the two-term name) will be used to compute the extrapolated boundary face value. Note that care should be taken when setting this parameter to true. Solving for a two-term extrapolated boundary face value requires simultaneously solving for the attached cell centroid gradient. This creates a system of equations. This system has the potential to be singular if there are multiple extrapolated boundary faces per cell; see MOOSE issue. The only time it's reasonable to expect a cell with multiple extrapolated boundary faces to yield a nonsingular system is if the vectors from the cell centroid to face centroid are parallel to the surface normals and none of the surface normals are parallel to themselves (e.g. imagine an orthogonal quad with three extrapolated boundary faces).

Another parameter in the MooseVariableFV template is use_extended_stencil. This is defaulted to false. When false, the gradient is computed using face values which are linearly interpolated between the current cell centroid and the neighboring cell centroids. When toggled to true, the face values are computed as a weighted function of the attached face vertices. This requires computing solution values at vertices which will be a function of all adjacent cells. This extends the stencil and increases the size of the Jacobian matrix. The benefit is supposed to be increased accuracy of the gradient computation. However, with the current implementation the vertex approach is actually less accurate (solution convergence of O(h^{1.5) as opposed to O(h}2) for the smaller stencil). This may indicate a bug in the current vertex-based implementation which hopefully a smart user will come along and fix.

Example Input File Syntax

To create a MooseVariableFVReal a user can do one of the following in their input file:

[Variables]
  [u]
    family = MONOMIAL
    order = CONSTANT
    fv = true
  []
  [v]
    type = MooseVariableFVReal
  []
[]

Note that a user must specify the type if they want to be able to set finite volume variable specific parameters like two_term_boundary_expansion or use_extended_stencil.

Input Parameters