[petsc-users] Solving advection equations implicitly

[Nishant Nangia]

We basically want something that is stable and non-oscillatory for any
given time step size.

A little more context: Q is a fluid density variable, which we are
currently updating using an explicit forward Euler step. This updated
quantity is later used in a conservative discretization of the
Navier-Stokes (NS) equations on a staggered mesh. We are using finite
volume/finite differences.

We observe oscillations in Q after a few time steps, which causes the
overall mass of the domain to change and breaks the linear solvers for NS.
We are experimenting with some strong stability preserving, TVD schemes to
update this density, but were thinking of trying an implicit update instead.


*Nishant Nangia*
Northwestern University
Ph.D. Candidate | Engineering Sciences and Applied Mathematics
Tech L386

On Mon, May 7, 2018 at 4:56 PM, Jed Brown <jed at jedbrown.org> wrote:

> Do you want it to be time accurate (implies CFL number is modest) or do
> you want very large time steps?  If very large time steps, why not
> steady state?
>
> Nishant Nangia <nishantnangia329 at gmail.com> writes:
>
> > Hi all,
> >
> > I want to implicitly solve a linear advection equation of the form:
> > dQ/dt + div(u*Q) = 0
> >
> > for a scalar quantity Q, with some known velocity field u. Note that it
> is
> > purely advection with no diffusion term.
> >
> > Is there a recommended solver/preconditioner combination to solve
> something
> > like this?
> >
> > *Nishant Nangia*
> > Northwestern University
> > Ph.D. Candidate | Engineering Sciences and Applied Mathematics
> > Tech L386
>
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