[petsc-users] multi-grid for anisotropy

[Jed Brown]

Justin Chang <jychang48 at gmail.com> writes:

> Hi all,
>
> I think I have asked a previous question related to this, and have
> seen other threads about related issues, but say I have this
> anisotropic dispersion 

Diffusion and dispersion are different phenomena.  Sounds like you mean
diffusion.

> tensor:
>
> D = (D_m + alpha_L*norm(v))*Identity + (alpha_L - alpha_T)*outer(v,v)/norm(v)
>
> The anisotropy of this tensor comes from the ratio of alpha_L/alpha_T and velocity v, and is mesh independent. That said, can tuning the multi-grid preconditioners parameters of GAMG/HYPRE/etc help prevent things like negative concentrations and violations of the discrete maximum principles?

Hell no!  Tuning an algebraic solver doesn't fix a non-monotone discretization.

That said, the linear solve could converge "from below", in which case
you might want to perform a cleaning step that fixes values by less than
the algebraic solver tolerance.
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