Matthew Knepley <knep...@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).
