[petsc-users] Ensuring non-negative solutions

[Jed Brown]

Gautam Bisht <gbisht at lbl.gov> writes:

> PETSc,
>
> I had few questions regarding adaptive time stepping inTS.
>
> - Can temporal adaptivity in TS ensure non-negative solution of a PDE?

If short steps are sufficient to prevent negative solutions, then it
can.  The simplest way is to set your own step acceptance criteria and
reject steps that become negative (or set a domain violation for the
function, in which case the solve will fail and the step will be
rejected, shortening the step).

> - For coupled multi-physics problems, can TS ensure non-negative solution
> for only one of the physics (eg. ensuring non-negative surface pressure for
> a coupled surface-subsurface flow simulation)?

Yes, as above.

> - Are there examples for such a case?

Not currently, but it would be good to develop some.  Depending on the
physical process by which negative values occur, it may be sufficient to
use an SSP integrator and respect some a priori step size criteria.

> At this stage I'm interested in finding out if ensuring non-negative
> solution is feasible and what would be required for such an implementation.
> If you could point me to some references that would be much appreciated.
>
> Thanks,
> -Gautam.
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