I read sometimes here in the forum, that to choose courant number around 0.5-1.0 for the time step size in PISO is a good choice... but in this case I could also you an explicit time discretization, what is the advantage from piso against an explixit algorithm?!?!

Good question.

By explicit algorihm, most people would presume that you mean something like a Jameson sheme. In which case the CFL number has the speed of sound in it, so you cannot make a direct comparison.

CFL(incompressible) = delta_t * vel / Length_scale CFL(compressible) = delta_t * (vel + c) / Length_scale

But let's assume, we are going to make an incompressible code explicit... I believe most of the commercial codes will let you switch on an explicit solver, (I have been told FLUENT can). The closest research code that I have seen is KIVA which can do explicit/implicit splitting of the convection and diffusion terms. (There is a logic here your diffusion shouldn't affect pressure waves).

The problem writing an explicit incompressible flow solver is that it ruins your PISO/SIMPLE/SIMPLEC/etc. derivation, full-stop. What you will achieve is a kind-of pseudo-compressibility solver (i.e. FIDAP-type solver), the coefficients in your pressure correction equation will only depend on temporal terms, since no one uses this approach it must be inferior.

Iain

ps for steady-state problems you should be able to push PISO/SIMPLE to 3.0 or so quite happily.