I have streamfunction and vorticity based model which gives me incompressible flow results.

How to convert this model into compressible?

Please help me.

The vorticity transport equation is derived by taking the curl of the incompressible Navier Stokes equations. Please check the derivation, and correct me if I am wrong.

yes sir, you are correct so now i need NS equation which can take compressible effects to simulate shockwave with turbulence.

shall i convert this vorticity-streamfunction based code to primitive variables based one (ofcourse, to get NS equation)?

please help me with suitable idea,.

thanks in advance

I do not know Why or What are you doing, are you writing a programme for academic thesis, research, or industrial needs..

I would not waste my energy trying to "convert this vorticity-streamfunction based code to primitive variables based one", you need to start afresh, take the book by Anderson, read the last chapter, it describes a flow chart for a 2D Finite difference compressible solver, which can be easily extended to 3D or get the book by Blazek and develop a 3D finite volume solver or the book by Hirsch or ...... You see, you have a good number of options and Only you can decide for the best option Good Luck

actually its going to be very difficult. It all depends on what algorithm you are using to solve incompressible flow. If the solver now is segregated, then it is not advisable to convert it into compressible solver.

The reason is compressible solver that captures shock is entirely different algorithm than what you have.

However, solver or solution method is just one part of over all solver. There are many other things like reading mesh, getting control volume information etc etc. If you use current code you could save time here.

But i am afraid for compressible flow you might have to write whole algo again.

I would suggest that make a list of reusable parts of current program, if after this you think it is worth adding into the current program, then go ahead.

sir

I am doing this for my research. I think, i should go for making a 2D code compressible code.

Can you tell me? how to capture shock wave and turbulence together? I have an energy spectrum which gives the isotropic turbulence initial data and now i need to merge the shock wave with this.

please help.

OK, you know the scope and objective of your research, I would suggest reading the last chapter of Anderson book, study the flow chart and see if it fits your research then roll up your sleeves. Keep the following book handy: C.A.J. Fletcher, Computational Techniques for Fluid Dynamics. Good Luck

Please correct me if I am wrong.

Since we dont seperate equation for pressure, we use vorticity stream funtion method to remove pressure for incompressible flow. where as incase of compressible flowl, we have equation of state to find pressure. So no need to go for vorticty streamfuntion method. You can solve based on primitive variable method.

you are definitely not wrong in asking this question. But it seems the question was what shall be done to change an incompressible solver which is based on vorticity formulation to compressible solver .

If one has to just convert results from u,v,w and vorticity to u,v,w and pressure, i believe it might be done without much hassle.

But since solver was incompressible and to convert it into compressible (a density based) would be big issue. Because in this senario you are change whole algorithm, not just results.

if someone want to stick to pressure based compressible than change won't be much. Pressure matrix won't be symmetric now and it could be solved with solved with suitable method.

Thank you. I understood.