Hi, guys, in your expereience, how many timesteps should be set in the sub-iteration in the dual-time calculation?

Dear Wil Turb,

I believe you are asking for the number of subiterations per physical iteration in an unsteady solver employing dual time stepping. Instead, I think you should be looking at options to terminate the pseudo--steady state solution in every physcial iteration. The points to be noted are as follows.

1. You can fix an arbitrary number of subiterations. This could be 10 or 20, and you could use it and get your answers. This works mostly, but you would not know to the extent your pseudo--steady state problem is being converged, it may not be actually achieving steady state and you are compromising heavily on time accuracy. If temporal accuracy is a concern, I believe that a fixed number of subiterations is never an option.

2. Another possibility which is more reasonable is to set a tolerance for the dual iterations. Well, again the tolerance is a user-choice, making it subjective but atleast the user has a better control on the convergence of the inner iterations. A typical preferred value is 1e-6, and some people may go upto machine precision.

3. Engineering applications look at an optimal tradeoff between accuracy and effort. Clearly, going for a low tolerance or high number of subiterations helps ensure design accuracy but then this could be non-optimal and lead to a larger effort. Going for a smaller effort means that you could end up with a lower time accuracy. A practical engineering solution is to employ a temporal error estimator (Look into the works of Kennedy, Carpenter and Vatsa) which can help decide a suitable termination criterion for the dual loop. Well, here too there is a need for some user intervention, but with some experiments a reasonably good termination criterion can be built.

It is therefore clear that all the three options to terminate the inner iterations are not completely universal, but the third choice seems to a practically viable and promising option. And in any case, you are looking to use (1) without really looking at temporal accuracy, my answer would be that the subiterations may depend on the problem and domain at hand, but 20 would not be a bad choice .....

Hope this helps

Regards,

Ganesh