[petsc-users] examples of DMPlex*FVM methods

[Ingo Gaertner]

2017-04-05 19:56 GMT+02:00 Jed Brown <jed at jedbrown.org>:

> Ingo Gaertner <ingogaertner.tus at gmail.com> writes:
>
> > Hi Matt,
> > I don't care if FV is suboptimal to solve the Poisson equation. I only
> want
> > to better understand the method by getting my hands dirty, and also
> > implement the general transport equation later. We were told that FVM is
> > far more efficient for the transport equation than FEM, and this is why
> > most CFD codes would use FVM. Do you contradict? Do you have benchmarks
> > that show bad performance for the (parabolic) transport equation
>
> What is the "parabolic transport equation"?  Advection-dominated
> diffusion?  The hyperbolic part is usually the hard part.  FEM can solve
> these problems, but FV is a good method, particularly if you want local
> conservation and monotonicity.
>

By transport equation I mean the advection-diffusion equation. This is
always parabolic, independent of whether it is advection dominated or
diffusion dominated. And the elliptic Poisson equation can be solved by
making it timedependent and converge to steady state, again solving a
parabolic equation. At least  this is how I learned the terms.
My impression is that everybody has his hammer, be it FEM or FVM, so that
every problem looks like a nail. You can also hammer a screw into the wall
if the wall isn't too hard.

Ingo

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