Hy there,

I use a time-explicit (5-stage Runge-Kutta) finite-volume code for unstructured grids for my PhD thesis. This is a compressible code, using a 2nd-order Roe scheme for spatial discretization.

This code is presenting slow convergence of velocity profiles, say an incompressible flat plate boundary layer flow.

What I would like to ask if this is usual for explicit codes. Also, there would be any work-around for that behaviour, that is, for accelerating convergence? I already have a "geometric" multigrid... what else could be done: implicit residual smoothing, preconditioning... ? Any suggestion?

Thanx a lot! Biga

Biga,

Most compressible methods are notorious of slow convergence (if at all) for incompressible problems since the matrix becomes ill-conditioned. There are some remedies in the literature (usually by using preconditioners).

Alternatively, stick to solution of compressible flows (Mach > 0.3).

Decoupling between the continuity and momentum equations, and stiffness, due to incompressibility is part of the problem, and can be helped by preconditioning, as was mentioned. What Mach number are you using? If it's too low, not only is your convergence bad, but the code may not even converge to the correct incompressible solution!

I am assuming you apply local time stepping, for steady-state problems? The definition of your local time steps may have a strong influence on convergence.

Residual smoothing certainly will boost the stability of your scheme and allows you to increase the CFL number for faster convergence. I am not sure how easy it is to implement with unstructured grids. A Gauss-Seidel method might be useful.

Also make sure to use appropriate cell geometries (hexahedrons) in regions where velocity gradients are predominant in a certain direction, e.g. in boundary layers.