I am wondering how people go about accelerating a time-dependent algorithm to steady-state? I am particularly interested in the situation where one is solving the time-dependent Stokes problem without the non-linear terms. I've been considering using the algorithm of Zienkiewicz et al (Int. J. Numer. Eng., v43, p565-583) but am only interested in the steady state solution (sans advection of the mesh after the velocities are found). Matthew

It's hard to answer because you have to make sure that your unsteady algorithm , your mesh and your boundary conditions will give you a steady state solution in the first place. Most of the time, the unsteady solution remains unsteady just because of the mesh you used. I would say, first run a true unsteady solution first, and make sure that your method and mesh and the boundary conditions will give you a steady state solution. Then, there are two general approach you can use: 1) fool around with the local time steps, that is to increase it to speed up the real time. 2) spend more time in the area where the solutions have difficulty in convergence. A good initial flow field guess also will reduce the computing time.

Hi,

For the convergence acceleration of time-marching algorithm, I think there are three popular methods. Local time stepping(Dual time steeping for unsteady problem), Local Preconditioning and Multigrid all work well. Conbination of two of the three methods will have very dramatical effect. You can read CFD Review 1995', or the papers of Marviplis(NASA Langley).