Derivation of the pressure-correction equation for compressible flows
 

Hi everyone,

I am working on pressure correction methods for flows with variable density (cavitation) and in this context I am trying to derive the pressure correction equation for compressible flows as it is proposed by Karki and Patankar or Senocak and Shyy.

In the references a relation between the pressure and velocity corrections is used which is in my opinion only valid for incompressible flows. In my derivation of the equation I used a deviant relation which can be obtained from the compressible momentum equations and hence get another pressure correction wich does not contain a convective term for the pressure correction.

From my point of view, my pressure correction equation should be valid for compressible flows but it does not reflect the convective nature (it is only a diffusion equation) for highly compressible flows. On the other hand I do not understand the choice of the velocity-pressure correction relation used by the references.

I made a little report explaining what I mean: http://eiscafe-di-lago.de/cfd-online/cpce_01.pdf

Can anybody help me?

By the way, does anybody have a pdf of the PhD thesis of Karki (A calculation procedure for viscous flows at all speeds in complex geometries)?

Thanks in advance!

Michel