Algorithms for solving the system of equations
 

Hi everybody,
I want to solve an axisymmetry 2D problem. After discretization of equations, I have a system of equations. The problem is unsteady state. I've used the TDMA, Gause-Seidel and SOR algorithms for solution of system of equations. But solution procedure is very time consuming. The number of my grids is about 10000-40000.

Is there anyone who recommend me a faster algorithm? I have used the CFD package like Fluent and OpenFOAM for same problems and those softwares were very faster than my code. What algorithms do these softwares use? I know the multigrid method. Could you recommend me any other methods?

Thanks in advance.