If we use SPMD and domain docomposition to calculate unsteady flow on distributed memory parallel computers, do we have to make sure that the calculations in different domains are advanced at the same time with the same time step size? If not, would the flow signals be propagated correctly across the domain interfaces?

Yes, you must have a spatially constant time step in order to get a physically correct transient solution. Not only that but your global time step size is set by the stabillity limit of your smallest cell. Hence big cells will use a much smaller timestep than they otherwise could. For a steady state solution, you are not intersted in a physically correct transient so not only each domain, but each cell can use a different time step, set by it's own stability limit.

Suppose a certain domain is slightly smaller than the others. Then the calculation in this domain may be faster than others. How can we make sure that this will not cause incorrect propagation of the flow signals?

Isn't this the challenge? Firstly you have to implement a synchronization and message passing system (off-the-shelf or DIY?) and use it to ensure all domains come together at the end of each time increment. Then you have to devise a method of dividing your domain up so that each piece takes approximately the same time to solve (or you'll just waste CPU time). You could have a small, lightweight lead process to do all the inter-process communication, or you could fold this work into one of the domains, which then becomes the lead domain.

You should have communication across domain boundaries (at least) once per timestep. If one domain takes less physical time to complete a time step than the others then it will just have to wait until the rest 'catch up'. Of course this time spent waiting is very ineffiecient, fortunatly there are several excellent (and free) applications which will divde your mesh into equallly (computationally) sized domains so that the problem is equally balanced between all processors. See the parallel computing section in this website's resources list

Hi,

Any of you dealing with three dimensional unsteady viscous flows for internal flows caused by instabilities due to vortex interactions on parallel machines? Could any of you put me in touch with some one working something close to this.