Does Dual time stepping with larger physical time step accelarates convergence for steady state solutions than Local time stepping?

Please comment

Regards Aditya

Dear Aditya,

DTS with larger physical time steps is not the way to accelerate convergence for a steady state problem. In fact it turns out that use of larger physical time step would cause a degeneracy in the time accuracy, even if you manage to get a solution. Also, many times a larger time step could lead to instability, thus not leading to a solution. The idea therefore is to keep a physical time step, which is optimal, not too high for instability and not too small for excessive computational time. The acceleration is then done within the DTS, where you use local time stepping etc... If you are using the same ideas you use for a steady-state solver inside the DTS, and you solve a steady-state problem, you are actually going for a little extra effort, compared to the steady-state solver, because you are handling two times. The use of DTS for steady-state problems is therefore more of a check to the code, in its ability to reproduce the results, rather than a practical use. If a generic code is written, it is therefore desirable to switch back to an ordinary steady-state solver for steady problems rather than using DTS.

I have also answered your related questions in regard to DTS in an earlier post, around Nov.4.

Hope this helps.

Regards,

Ganesh

Hi Ganesh, I knew it did not make a reasoning but was rather a wishful thinking that DTS would help. Actually the problem is that in our code, the residues make a 2 to 3 decade fall and almost remain stagnant after that. Can DTS give me a further fall in residues. So thats not exactly a convergenc accelaration i guess.

Aditya

Without dual time, you are choosing the global minimum as the time step everywhere in the field. Local time stepping (using dual time) simply speeds up convergence by increasing the pseudo time step based on local stability. It's very unlikely that this will give you a lower residual. In fact, the convergence with global time stepping will likely be more benign, and local time stepping would likely worsen the situation. There is, however, a small chance that local time stepping might help. If your convergence troubles are caused by a physical instability (unsteadiness), local time stepping may possibly counter-act that problem, because you are not solving in real-time anymore. It's possible, but I wouldn't count on it. Anyway, considering the advantages of local time stepping (and the relative ease of implementation), it's imperative that you implement it in any case. No need to contemplate on possible effects on residual stagnation. Just do it and find out.

Dear Aditya,

The residue fall for the outer loop (or physical time) is of no relevance because the problem is unsteady. The relevant residue fall is in DTS, which should theoretically be zero and practically be of the order of 1e-6. However, researchers have different opinion on this tolerance and even 1e-2 have been adopted. Generally, this happens when you are on a finer grid, and more so for a viscous problem especially, so it does not come as a big surprise. Therefore, to make sure that your code is really bug-free for an inviscid problem and otherwise , you could check out DTS on a coarser grid and see if a good convergence is obtained, after incorporating local time stepping, in case you have not.

Hope this helps

Regards,

Ganesh