[petsc-users] examples of DMPlex*FVM methods

[Jed Brown]

Matthew Knepley <knepley at gmail.com> writes:

> On Thu, Apr 6, 2017 at 8:32 AM, Jed Brown <jed at jedbrown.org> wrote:
>
>> Matthew Knepley <knepley at gmail.com> writes:
>> > Okay, that makes sense. If I do not have fluxes matching the sources, I
>> do
>> > not
>> > preserve montonicity for an advected field. I might need this to machine
>> > precision
>> > because some other equations cannot tolerate a negative number there. I
>> will
>> > write this one down.
>> >
>> > Why do I need it "for a projection in a staggered grid incompressible
>> flow
>> > problem".
>> > This would mean I satisfy (I think)
>> >
>> >   \int_T div p = 0
>>
>> Matt Knepley can take the divergence of a scalar.
>
>
> Yes, I forgot the grad. It is crazy here. Same question.

It's crazy here too, but as far as I know, I didn't wake up this morning
with discretization amnesia.  Recall that pressure projection is derived
by taking the divergence of the velocity equation and using div u = 0 as
an identity.  If you want a velocity field that is element-wise
divergence-free (as is desirable for any advected field) then you need a
compatible pressure space.  With staggered FD, that pressure space is
the piecewise constants.
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