[petsc-users] Solving advection equations implicitly

[Zou, Ling]

On Mon, May 7, 2018 at 4:15 PM, Nishant Nangia <nishantnangia329 at gmail.com>
wrote:

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

TVD upwind + 1st order BDF (BDF1)

As Jed already pointed out, there is no strong stability-reserving (SSP)
scheme with oder > 1.



>
> 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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