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

[Jed Brown]

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

> Yes, all of that sounds correct to me,
>
> No I haven't tried embedding the column integral into the RHS, right now I
> am unable to think how to do this without the solution of the previous
> intermediate stage. Any ideas are welcome,

Do you have some technical notes on your present formulation?  I think
it just amounts to performing the integration and then evaluating the
differential operator using results of that integral.

> Thanks,
>
> On Wed, Oct 9, 2019 at 4:18 PM Jed Brown <jed at jedbrown.org> wrote:
>
>> 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?
>> >> >>
>> >>
>>