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Old   September 10, 2006, 03:52
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dontknow
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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?!?!
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Old   September 21, 2006, 09:01
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Iain Barton
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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.

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