Explicit Duel Time Stepping
 

I have implemented DTS in my code which is 3D multiblock structured. Explicit formulation. However testing out on simple cases, I found that the computational step i.e the psuedo time step/ no. of sub iterations has to be near the time step corrosponing to the smallest cell in the Grid. So essentialy for unsteady problems, DTS and global are eating out almost same computing time. Can anyone comment on it?

THanks

Aditya

Re: Explicit Duel Time Stepping
 

Dear Aditya,

The basic idea of introducing the DTS for unsteady problems is the fact that the problem becomes pseudo-steady, and hence convergence acceleration devices can be employed. Now in your case, the DTS is explicit, and you do not seem to use any convergence acceleration devices. And being explicit, you are bound by a stability criterion, and this is why you seem to get the computational time step closer to the time step corresponding to the smallest cell in the domain. You could have also run your test case without DTS in an explicit mode. You would end up in getting the same results. The fact that "DTS and global are eating out almost same computing time" is a conclusion, is a consequence of two factors- An explicit formulation bound by a stability criterion and the absence of convergence acceleration devices.

The possible remedies would include 1. Still explicit, but with convergence acceleration using multigrid, residual smoothing, enthalpy damping etc ... 2. Implicit, preferably matrix-free formulation with/without the aforementioned devices.

I work with implicit formulation, which does not have a stability bound, atleast in a linear sense, and use local time stepping in DTS. I have seen that for problems such as an oscillating airfoil problem in 2D, the use of implicit procedure speeds up drastically compared to an explicit procedure.

Hope this helps

Regards,

Ganesh

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