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

[Manuel Valera]

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?

Thanks,










On Wed, Oct 9, 2019 at 3:24 PM Jed Brown <jed at jedbrown.org> wrote:

> Manuel Valera via petsc-users <petsc-users at mcs.anl.gov> writes:
>
> > Hello,
> >
> > I have a set of equations which are co-dependent when integrating in
> time,
> > this means the velocities u,v,w need a component from the Temperature and
> > Salinity integration at the same intermediate step. Same for Temperature
> > and Salinity, which need the current velocities (at the intermediate time
> > stages) to be computed accurately.
>
> There's nothing special about having different fields.  Just evaluate
> the RHS function of the coupled system.  There are examples (e.g.,
> ts/examples/tutorials/ex9.c) of doing this for systems like shallow
> water (momentum coupled with thickness).
>
> > My question is, how to feed the information of the updated temperature
> > inside the velocity, and vice-versa? this would be equivalent, I think,
> to
> > obtaining the intermediate stages of the time integration so they can be
> > the input for the next intermediate stage.
> >
> > Thanks,
>
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