[petsc-users] PetscFV types

[Jed Brown]

Matthew Knepley <knepley at gmail.com> writes:

> Sure. PetscFV is mostly an exercise for me to determine if the meshing
> and data layout infrastructure below can support finite volume
> methods, so the FV methods that it does support are rather
> rudimentary. My understanding of FV is quite limited. "upwind" is just
> the naive, first order FV method with pointwise Riemann solves for
> each local face. I called it upwind since we just update the state
> with the upwind data. I guess I could have called it "gudonov" as
> well. The "leastsquares" uses a least-squares reconstruction of the
> state over cell+neighboring cells (closure of the star of the faces)
> to try and achieve second-order where possible. I guess I could have
> called this "reconstructed".

I agree with Pierre that the terms should be revised.

Upwinding is what a Riemann solver does (in an appropriate sense for systems).

There are multiple reconstruction methods.  I would classify by reconstruction (none, least squares with various neighborhoods and limiting types, WENO), and flux methods (approximate Riemann solvers).

Many reconstruction schemes can be decoupled to a linear step (least squares) and a nonlinear limiter, but methods like WENO combine these (albeit most popular on structured grids).