I want to program a coupled solver to solve the continuity equation, navier-stokes equation and the energy equation simultaneously. But I face the difficulty to linearize the non-linear equation system and to build the coefficient matrix. Could you give me some hints or introduce a good book on this topic for me?

Thanks a lot!

Have a look at John Anderson "Computational Fluid Dynamics" In chapter 10, He develops a 2D solver for the compressible Navier Stokes. Good Luck and Cheers. When I used it, I did not face any of the problems you describe.

Thanks a lot, Ahmed.

I am looking for the book of Anderson