Small influence of convection in PISO if Courant number is small
I've been lokking on OpenFOAM's PISO for some time. With the help of this community I've found detailed information in Prof Jasaks PhD thesis and his paper on numerical simulation of flow. But there is still one question open:
OpenFOAM's PISO calculates H and therefore rUa just one time in each time step after solving the momentum predictor. In all following PISO-loops these terms are treated as constant. Prof. Jasak explains this with the small influence of convection compared to the pressure-velocity coupling if the courant number is small enough.
Okay, heuristically I see this point. But from a mathematical point of view: why is this true and is it possible to give a critical value for the courant number ?
Does anybody know an answer or a paper where I could get more information about this ?
Best regards and thank you very much,
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