From the cfd book of John Anderson, Jr, I have tried to follow the solution technique for converging-diverging nozzle flows by using of MacCormack technique. But I found the problem about the purely subsonic case. This book did not show the solution of this case by using the governing equations in conservation form. So I have developed my code base on the governing equation in conservation form and it gave the correct !! solution for the case with normal shock (but the numerical solutions had some discrepancy). When I perform the purely subsonic case, the numerical solutions was wrong--differ from the solution in the foregoing section of that book. My questions are 1. Can the governing equation in conservation form be used with subsonic flows? 2. If the answer of the first question is no, does it mean that the conservation equations are appropriate for case with shock only and the non-conservation equations are appropriate for the case without shock. 3. If the answer of the first question is yes, what is the possible error in my code? 4. Where can I find the excellent and clear explanation about using and caution of these two formulations of governing equations of fluid flow?

The governing equations (Euler equations I assume) are valid both for subsonic and transonic flows.

The MacCormack scheme isn't very good at cases with low Ma numbers though. If your Ma number goes below say 0.3 you will probably get stability/convergence problems with that scheme.

Hi,

I programmed the scheme for CD nozzle. my inlet was supersonic and outlet was subsonic. The shock was best resolved by Roe's scheme. For low mach no. roe's scheme blows up bcos the jacobian of flux vector become near to singular....however mac-cormack works if more dissipation is added. Conservative form is the mother of all forms. It will work in any situation....compressible/incompressible,you must obiviously use correct the scheme. For compressible flows conservative form is recommended.However I have seen papers where people use finite difference for compressible flows( with some correction terms). Follow this link if you need to know more about conservative/non-conservative forms. http://personalpages.umist.ac.uk/sta...hydr/INDEX.HTM

Also try other CFD books by Hirsch(this one is good), D.A. Anderon, Pletcher.

Hope this helps.

abhijit

Hi, Maybe you will be interested to see my solution for technique presented in John Andersson book:

see: "Prandtl-Meyer expansion wave solution" PDF file on my web page:

http://panoramix.ift.uni.wroc.pl/~maq

Maciek

please send me the solutuions. thnk you.

i am a post graduate student.i am doing a course in CFD

let me know the solutions of the above problems edpecially "sub sonic-super sonic flow in CD nozzle", if possible.