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

[Manuel Valera]

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,

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?
> >> >>
> >>
>
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