If you search for (-i) "boundary" in ts/ex11.c you will see several examples of setting BCs with ghost cells in FV.

Don't worry about hyperbolic per se. The PETSc interface is very abstract: G(x,xdot,t) = F(x,t), or something like that. You can decide which side of the equation to put each of your terms.

I'm not sure what you mean by derivatives of the context variables, but I see that FV does not seem to have the auxiliary variable support that FE has, where we take spatial derivatives of anything that you want.

If you want to have context variables in your cells so that you can take derivatives in your Riemann solver then you could add dummy variables to your system like Identity*q = Q. Then q would be in the L/R state variables.

Hope this helps,
Mark


On Mon, Jul 20, 2020 at 5:28 AM Thibault Bridel-Bertomeu <thibault.bridelbertomeu@gmail.com> wrote:
Dear all,

I have been studying ex11.c from ts/tutorials to understand how to solve an hyperbolic system of equations using PETSCFV. I first worked on the Euler equations for inviscid fluids and based on what ex11.c presents, I was able to add the right PETSc instructions in an already existing in-house code with different gas models  to solve the problems in parallel (MPI) and with the AMR capabilities offered by P4EST.

Now my goal is to move to Navier-Stokes equations. Theoretically the system is not completely hyperbolic and can be seen as one with an hyperbolic part (identical to the Euler equations) and a parabolic part coming from the RHS diffusion terms.
I have been looking into the manual and also the sources of PETSc around the DM, DMPlex, DS and FV classes but I could not find anything that speaks to me as "adding a RHS to an hyperbolic system of equations" or "adding a source term to an hyperbolic system of equations". What's more, that source term depends on the derivatives of the context variables ... 

I wanted to know if anyone maybe had a suggestion regarding this issue ?

Thank you very much in advance, 

Thibault Bridel-Bertomeu
—
Eng, MSc, PhD
Research Engineer
CEA/CESTA
33114 LE BARP
Tel.: (+33)557046924
Mob.: (+33)611025322