[petsc-users] Solver/Preconditioner for advection diffusion equation

[Matthew Knepley]

On Mon, Oct 13, 2025 at 2:52 AM Miguel Salazar <miguel.salazar at corintis.com>
wrote:

> Hi,
>
>
>
> Is there an off-the-shelf solver or preconditioner in PETSc to handle
> advection-diffusion equations with large Peclet numbers (Pe > 2000)? The
> equations are solved with the FEM and ideally, one could just use the
> solver through the PETSc settings without having to set up any mesh
> hierarchy or partitioning (no geometric multigrid or domain decomposition).
> I read that the Approximate Ideal Restriction method is appropriate for
> this kind of problems, but the documentation is scarce. Any pointers are
> welcome.
>

Hi Miguel,

We are in the process of integrating PFLARE (
https://urldefense.us/v3/__https://gitlab.com/petsc/petsc/-/merge_requests/8776__;!!G_uCfscf7eWS!ZJ-UU8WRuA_VDt1Dm2hWiknuosHNCBYsXeE5bRhQvYUKO5f9hYqWqO0EPybEBT8sF5mV_wS98QMoE9AUh7nc$ ), which is an AIR
package from Steve Dargaville at Imperial. Hopefully in the next few days.
You could try out the branch until then and let us know if you have
problems.

  Thanks,

     Matt


> Thanks,
>
> Miguel
>
>
>
>
> *MIGUEL ANGEL SALAZAR DE TROYA*Head of Software Engineering
> *miguel.salazar at corintis.com* <miguel.salazar at corintis.com>
>
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