Hello, everyone:

Now I am going on my thesis. But I meet one problem, which is how to solve the hyperbolic eqs coupling with parabolic eqs.

Thank you very much for your advice?

In fluid flow, always HYPERBOLIC is in time, and PARABOLIC is in space. Generally the whole eqs system is hyperbolic in t (compressible flow), you need use time marching scheme. But for incompressible flow, the nature is mainly elliptic (parabolic is a subset), then thare are pressure correction methods and artificial compressibility methods to choose.

Thanks a lot for your reply! Maybe my last question was not clear. Would you like to read it again?

Here is my question in detail. In the PDE system, one PDE is hyperbolic, and the others are parabolic. It is 2D in space, but there are no time terms in it. How can I get convergent numerical results from this system?

For the hyperbolic equation, you only use upstream condiction to march along X; for Parabolic equation, You will also need two BC in Y. Independently marching, and check if the computed two BC in Y converge. do the two BC values in parabolic come from the hyperbolic solution?

Thank you very much! I will try it as you said. The following is the thing related to your last reply and my new questions.

The b.c. of the parabolic PDEs is the same as that of hyperbolic PDEs. But one b.c. is the result from one elliptic PDE. It means that I should solve the elliptic PDE to get one b.c. for the parabolic and hyperbolic PDEs system. Can I solve these equations together? Otherwise it is hard to get good result by the decoupling way, isn't it?