[petsc-users] PetscFV types

[Matthew Knepley]

On Fri, Sep 18, 2020 at 4:01 AM Pierre Seize <Pierre.Seize at onera.fr> wrote:

> Hello,
>
> I do not understand what are the two available types for the PetscFV
> object : "upwind" and "leastsquares", because to me those two properties
> describe different parts of the Finite Volume formulation. Could someone
> explain, or give me some references ?
>

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".

  Thanks,

     Matt


> Thank you
>
>
> Pierre Seize
>
>

-- 
What most experimenters take for granted before they begin their
experiments is infinitely more interesting than any results to which their
experiments lead.
-- Norbert Wiener

https://www.cse.buffalo.edu/~knepley/ <http://www.cse.buffalo.edu/~knepley/>
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