[petsc-users] TS_SSP implementation for co-dependent variables

[Jed Brown]

Manuel Valera <mvalera-w at sdsu.edu> writes:

> Sorry, I don't follow this last email, my spatial discretization is fixed,
> the problem is caused by the choice of vertical coordinate, in this case
> sigma, that calls for an integration of the hydrostatic pressure to correct
> for the right velocities.

Ah, fine.  To phrase this differently, you are currently solving an
integro-differential equation.  With an explicit integrator, you should
be able to embed that in the RHS function.  With an implicit integrator,
that causes the Jacobian to lose sparsity (the column integral is dense
coupling) so it's sometimes preferable to add pressure as an explicit
variable (or transform your existing variable set as part of a
preconditioner), in which case you get a differential algebraic equation
(the incompressible limit).

Have you tried embedding the column integral into the RHS function to
make a single unsplit formulation?

>  I had RK3 working before and SSP is much more stable, i can use way bigger
> DTs but then i get this asynchronous time integration. With RK3 I can
> operate in the intermediate states and thus I can advance everything in
> synchronization, but bigger DTs are not viable, it turns unstable quickly.
>
> On Wed, Oct 9, 2019 at 3:58 PM Jed Brown <jed at jedbrown.org> wrote:
>
>> Is it a problem with the spatial discretization or with the time
>> discretization that you've been using thus far?  (This sort of problem
>> can occur for either reason.)
>>
>> Note that an SSP method is merely "preserving" -- the spatial
>> discretization needs to be strongly stable for an SSP method to preserve
>> it.  It sounds like yours is not, so maybe there is no particular
>> benefit to using SSP over any other method (but likely tighter time step
>> restriction).
>>
>> Manuel Valera <mvalera-w at sdsu.edu> writes:
>>
>> > To correct for the deformation of the sigma coordinate grid... without
>> this
>> > correction the velocity become unphysical in the zones of high slope of
>> the
>> > grid. This is very specific of our model and probably will be solved by
>> > updating the equations transformation, but that's not nearly close to
>> > happening right now.
>> >
>> > On Wed, Oct 9, 2019 at 3:47 PM Jed Brown <jed at jedbrown.org> wrote:
>> >
>> >> Manuel Valera <mvalera-w at sdsu.edu> writes:
>> >>
>> >> > Thanks,
>> >> >
>> >> > My time integration schemes are all explicit, sorry if this a very
>> >> atypical
>> >> > setup. This is similar to the barotropic splitting but not exactly, we
>> >> > don't have free surface in the model, this is only to correct for
>> sigma
>> >> > coordinates deformations in the velocity field.
>> >> >
>> >> > From how i see it this could be solved by obtaining the intermediate
>> >> stages
>> >> > and then updating them accordingly, is this not possible to do ?
>> >>
>> >> Why are you splitting if all components are explicit and not subcycled?
>> >>
>>