Matthew Knepley <[email protected]> writes: > On Thu, Apr 6, 2017 at 8:32 AM, Jed Brown <[email protected]> wrote: > >> Matthew Knepley <[email protected]> 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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