[petsc-users] PetscFV without ghost boundary conditions

[Jed Brown]

Thibault Bridel-Bertomeu <thibault.bridelbertomeu at gmail.com> writes:

> Sorry I wasn't clear I think.
> I was thinking that for finite volume codes, you have two options: either
> you use ghost cells that you fill up with the appropriate primitive state
> for the boundary condition, or you directly enforce the boundary condition
> at the face.
> In the PetscFV examples, the DM_BC_NATURAL_RIEMANN type of boundary
> condition with ghost cells is always used, but what about _not_ generating
> the ghost cells and using a DM_BC_ESSENTIAL to enforce the boundary
> condition directly at the face (or at the quadrature points on the face if
> you will) ?

Essential boundary conditions change the function space in which you seek a solution. There is no dof at the face in an FV method, so how would you propose modifying the function space.

Also, FV methods with higher than first order require a reconstruction (generally nonlinear) using neighbor cells to create a richer (usually piecewise linear) representation inside cells.