Is this the "checker board" problem?
 

Hi,

I've been using my 2d fractional step FVM NS solver to solve different problems. Now, I'm solving flow past square cylinder. Everything is ok at Re=100. However, at Re=400 onwards, there is oscillation of velocity u at from left to right ie u along horizontally is varying up and down e.g. 0.95,0.9,0.925 ... 0.8,0.75,0.77... although the trend is overall decreasing. Only close to the cylinder (upstream) will it be strictly decreasing.

A closer look shows that it is due to the pressure, which is oscillating e.g 0.2 0.05 0.18 0.06 ....

Is this the so called "checker board" problem? But Rhie Chow interpolation has been incorporated in the current scheme (Ham JCP (179) 2002, pp469) so this shouldn't happen. different outlet BCs such as du/dx,dv/dx=0 and convective BCs have been used. Similarly, far stream distances are very large. p is fixed at outlet and at inlet, u=1, p is extrapolated from interior.

Some things I've noticed:

1. oscillations decreases as more cells are present in the x direction 2. the higher the Re, the more severe the oscillations, assuming the no. of the cells are equal. 3. 1st few steps are ok but as time proceeds, oscillations start...

Re: Is this the "checker board" problem?
 

Hi, By seeing your values it looks like your problem has become unsteady vortex shedding.) so it is strugling to converge as steady state problem.

Re: Is this the "checker board" problem?
 

hi, can you explain further what do you mean? Btw, the oscillations happen upstream of the cylinder. Moreover I've encountered this problem when solving for an airfoil like body, which should be a steady state solution....

I am wondering if it could be my discretization, central differencing....