I am trying to implement a Dual Time Stepping strategy for my DNS code for full NS in cylindrical coordinates. The strategy is very simple and I have already used the method with different codes (aerodynamic calulations), however I am having a very strange behaviour this time: when I reduce the physical time step, which is an input data, the dual iterations do not converge very well: the rms of energy residual immediately drops, but then remains anchored to a certain value. This asintotic value should become smaller when reducing the physical time step, but in my case it becomes larger giving me the impression that convergence is not achieved ! What is strange is that the solution I got seems good!!! Does anybody know any explanations?

In dual time stepping, the physical time derivative appears as a source term in the equations you are solving. At least I am assuming that you do it that way. This source term can become quite large for small time steps, which may be the cause of your instability.

Many thanks. I think you are right, but why doesn't the code blow up?

What exactly is the residual that you monitor, I mean is that the convergence history within a time step? In dual-time iterations your are supposed to get a converged solution for each time step. Does the behavior you describe appear within each time step? One thing you need to know about time stepping is, that as you decrease the size of your time step, the physical behavior is more and more resolved (assuming consistent discretization). You will generally observe that the pseudo-time residual jumps up at the beginning of each time step, but then decreases, as the solution at the next real-time is obtained. Now, the smaller the time step, and the closer you get to resolving the physical behavior, the smaller is that initial jump in the residual. The final residual has a lower limit by the numerical precision. So you can see how the total drop in unsteady residual within each time step is reduced as the real-time step is decreased. This is normal and does not mean that your solution is bad. It simply means that your time step is so small that there is not much change between two consecutive time levels. Is this what you observe?