hi all. i have written a 2d ns solver using the projection method for pressure in the primitive variables. i can run my simulation around a square for Re>100 and it shows the karman vortices. however for Re<100 the code gives all garbage! could somebody enlighten me on this? thanks.. lost soul.

Hi Lostsoul (hope this is not your state),

your question is the well known Stokean paradoxon of creeping flow. In a limited flowfield there is no solution for Re->0 as the flowfield has a singularity at infinit distance from the cylinder. See for instance: Kaplun, Lagerstrom "Asymtotic expansions of Navier Stokes solutions for small reynolds numbers" J. Math. Mech. Vol. 6, 585-593. And if you know German: Gersten, Herwig "Stroemungsmechanik", Vieweg Verlag gives a brief introduction to this problem.

hi fabian! thanks a lot for the feedback.i am surely getting back my lost confidence well.. umm. i shall surely refer the paper that u have mentioned. btw. do u have any idea how i can make my code work for small Re No? i want to simulate the laminar flow around the square where are no karman vortices. my code starts garbaging below 60!! thanks a lot for all. less-lost soul

Hi less-lost soul,

I am not actually an expert in this topic, but for my knoledge you should try to put your outlet boundary as far as possible from the square (in theory at infinite distance). Good luck. But it may be better looking into the theory about creeping flow.

I guess there are probably two ways to deal with low Re in the projection method:

(1) in the 1st step of projecting the velocity, solving the viscous terms implicitly, i.e. mv the viscous terms to the LHS;

(2) Or just simply reduce the time increment.

Let me know if these work. Good luck.

Tony