I try to solve the energy equation(2D),including the convective term and maximum Pe is about 50,000. I have used the ADI method, however, the time step has to be very very small for large Pe. I also followed the split formulation, which is given by Fletcher on "computational techniques for fluid dynamics" . Although the method is said to be unconditional stable (I think it is for uniform grid), I still have to use small time step to get reasonable result. Is there anybody who knows the better way to solve such porblem? Thank you.

Hi There!

Why don't you try to use the multigrid method to solve your 2D flow implicitly in time? Multigrid methods are also easily implemented on massively parallel machine.

See for example:

Press and Teukolsky, 1991, in Computers in Physics (sep/oct 1991) page 514-519 and also (Nov/Dec 1991) page 626-629

and the references therein.

Cheers, Patrick.