Hi, all. My code use colocated grid and SIMPLE scheme. So, I have used Rhie and Chow's pressure correction in calculation of mass flux for prevent checker board problem. Thesedays, I add Free-surface logic. (2-fluid system) e.g ; gravitational force added as follows.

Source term - rho*Volume/Fn^2 in W-momentum (3D) As you know, by this force, pressure become Total. But, (except low-Rn) Checker board problem appeared. I just guess that pressure interpolation at surface has some problem...

Is there any-CURE ? Please, help me. (I really don't want to change my code to staggered.)

what is your density ratio.

You may need a bounded scheme to do interpolation at the interface, i.e. what's the density ratio? Because Rio*Vol/Fn*2 is much different here.

The problem may not be chess board pressure at all.

just comment.

hi there,

if you're using the collocated scheme, the fluxes satisfy continuity exactly ( divergence free), but the cell-center velocities do not. Check the level of divergence for the cell-center velocities and see if this it is appropriate, or if some regions of the flow have high divergence associated with them. If so, iterate on the cell-center field to bring the divergence down to an acceptable level. Now, it may be possible that the condition for the pressure at the boundary are causing these problems. Right now, I really don't know what is the best approach to determine P on the boundary: 1- dp/dy = 0.0 ?? 2- Make an interpolation from the interior points ?? 3- Use the y-momentum equation to derive something for the dp/dy ?? The 3rd approach might have more physics associated with it, but still it would be an approximation.

I hope this might help, Sincerely,

Frederic Felten.

Hi there,

Some people already knew the problem of Rhie-Chow's method when body force is included in the momentum eq.

Usually body force makes the pressure field highly non-linear. For example let's think about natural convection in a square cavity with hot top wall, cold bottom wall, and two adiabatic vertical walls. You see flow field is stationary, but pressure is quadratic in vertical direction. This pressure gradient term can make face velocity non-physical if grid scale is not compatible to the 3rd derivative pressure term added into a central-differenced face velocity.

I recommand you to reduce pressure term of Rhie-Chow scheme if it is very large compared to central-differenced face velocity.

If you have a problem on the wall boundary, you should use higher order pressure extrapolation such as linear or quadratic. Or you can add body force term into wall pressure.

Sincerely yours, Jongtae Kim

Thanks.

My density ratio is common ; rho/rho_ref. so, in air cell, rho is rho_air/rho_water and in water cell, rho_water/rho_water. naturally, at interface, rho=rho_water*vof+rho_air*(1-vof) ; vof means volume of fluid(water)

AND, I understood MR. Kim 's comment. BUT, How can I reduce pressure ? if there were no gravitational force, it could. but, it can not make free-surface wave.

Is there any method ? anyway thanks again.

Hi name,

Your name is Name? Sorry just because of surprise.

No, no, no What I mean is reducing the magnitude of pressure damping term in Rhie-Chow scheme.

You said you had checker-boar pressure field in your solution. How about velocity fields? Do you think it is physically reasonable? If velocity vecors somewhere in your computational domain are random, The cure is what I said.

Please check it and reply Thank you

I have also that problem in velocity field.(especially in V-velocity) ordinaly, non-dimensional presure has about -1 to 1. in gravity force, it depends on outer bottom size ; it means maximum pressure can be 20 or more. I think this big variable affects Rhie & Chow's correction term. (am I wrong ?)

reply plz. thanks

This is a well known problem and can be easily sorted out if you also consider the extra body forces in Rhie and Chow formula.

Really ? Can you tell me more information(method, reference, etc. ...) ?

PLZ.....