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

[Manuel Valera]

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 ?



On Wed, Oct 9, 2019 at 3:40 PM Jed Brown <jed at jedbrown.org> wrote:

> Manuel Valera <mvalera-w at sdsu.edu> writes:
>
> > Thanks for the answer, I will read the mentioned example, but to clarify
> > for Barry I will schematize the process:
> >
> > At time n, the program need to do all of these at once:
> >
> >    1. Solve T as a function of u,v,w
> >    2. Solve S as a function of u,v,w
> >    3. Solve rho density as a function of T,S
> >    4. Derivate a correction of the velocity fields from the density
> >    5. Solve u,v,w being corrected by the density field
> >
> > What I have implemented so far:
> >
> >    1. Advance TS1 to solve for T
> >    2. Advance TS2 to solve for S
> >    3. Solve rho and calculate correction
> >    4. Advance TS3 to solve for u,v,w
> >
> > Or, altenatively:
> >
> >    1. Advance TS to solve for T,S,u,v,w at the same time.
> >    2. Solve rho and calculate correction
> >
> > Both implementation are lacking the feedback from the T,S <-> rho <->
> > Velocities interaction, and is creating problems when using a bigger DT.
> >
> > All the systems from the first numeration are different algorithms, and
> > each TS in the 2nd numeration generate a different RHS.
> >
> > What Jed is suggesting is to create an overarching routine that does all
> > that is the first list under one single step?
>
> TSSSP isn't SSP or high order with ad-hoc coupling procedures such as
> the above.  If you're in a parameter regime that is stiff (e.g., typical
> regime in which barotropic splitting is popular), I would suggest
> putting the semi-implicit component into a preconditioner or
> Rosenbrock-W Jacobian approximation so that you can preserve the
> desirable accuracy and stability properties of the method.
>
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