[stephan]

hi,

after months of simply using compressible flow solvers (rhoTurbFOAM) i was wondering if somebody might be able to explain why DpDt=DDt(phi/rho,p) is written the way it is?
especially the "phi/rho" is pretty unclear for me?
i hope DDt(phi/rho,p) actually is really
phi/rho*DDt(p)+p*DDt(phi/rho) otherwise i am really confused.
i hope somebody might explain what this is all about or at least could give me a hint where to search in literature.
thanx in advance
regards
stephan

[stephan]

hi,

any help would be really appreciated!
regards
stephan

[hjasak]

Well:

DpDt = ddt(p) + U . grad(p),

right? The way to write it in the conservative FVM is to go to the strong conservative form, because

U . grad(p)

carries a non-conservative discretisation error. Thus:

DpDt = ddt(p) + div(U p) - p div(U)

All clear so far? Now, we need the div terms. In the FVM it is the mass conservative flux that is essential for all calculations. Thus for the div(U p) you want the normal way of doing things, i.e. using the face flux instead of interpolated velocity.

But what about div(U)? For consistency, you should not just interpolate the U: instead, do flux/rho, and take a div of that. This equals div(U) but the discretisation error is consistent. To make things better, you can interpolate rho onto the face with more consistency with the density equation, but that's another story...

See it now? As an exercise, stir in the moving mesh terms now

Hrv

[stephan]

hi,

at first - thanks a lot...
so i guess my misunderstanding was that DDt(a,b) is something like a*DDt(b)+b*DDt(a) (this idea came from the behaivior of ddt(a,b)) instead of ddt(a)+b.grad(a).

maybe you could please say some things about "another story..." because i guess this will hit some other problems of my solvers.


regards
stephan