checker board at free-surface
 

at free-surface interface... because of defferent density, vertical directional velocity (3D) distribution has checker board problem. my scheme is SIMPLE, HRIC, ... Can I fix that ?

Re: checker board at free-surface
 

What is your density ratio. Are you using a conservative or non-conservative form of the equations. Are you using surface tension? Is it large?

If you look at your pressure correction equation and you see that you have density within it, there is a way to take it out. Just derive the pressure correction equation and try and cancel out the density. It will.

This may be only half your problem. I don't really know. At free surfaces the surface tension force puts a discontinuity in pressure. If you have a good discontinuous coefficient solver than you should be ok. I.e. maybe multigrid. If not then your solver will try and smooth out your pressure discontinuity and place the discontinuity on the velocity field. To solve this , well I don't know, but my best quess would be to look at the solver. Ie. throw out stone :)