I have a problem where I have two stationary free surfaces. I use the continuity eqn. to compute what the velocity should be on the free surfaces every iteration. The problem is that I have alot of convergence problems with this case. Does anyone have any experience with these types of problems or any suggestions on how to rid myself of these convergence issues? I am using a SIMPLE like algorithm and solving for u,v, and p in a 2D axisymmetric geometry. Any help would be greatly appreciated.

Hi Chuck

I don't know what exactly your problem is, there are certain bits and pieces of the treatment of the free-surface that are always troublesome. The major problem is usually related to the implementation of the mass conservation in the cells containg the free-surface.

First of all. What are you doing with the pressure boundary condition at the interface ? If you are using Simple I supose you are prescribing the value of P at the free surface and setting the pressure correction as zero at the cell containg the interface. Is that correct ? If so you MUST make sure that the implementation of the continuity eq. in theses cell is correct otherwise you end up loosing mass or having convergence problems.

When you are using the continuity eq. to ensure mass conservation in the cell containing the free surface you have to be be aware that somethimes a cell can have 2 empty neighbours cells. In this case when you use the continuity eq. you end up with two unknows instead of one. What usually is done is to consider rho.Ui.Ai=rho.Ui+1.Ai+1 (where Ai is the area tranversal to i) for each direction to solve the problem (the original report of the MAC method - LA3425, Los Alamos, 1966 - contains a nice explanation of that, as well as the implications of using this aproximation).

I don't know if this can help you.

Cheers

Neyval

Neyval, thanks for the response to my problem. I use a variation of the SIMPLE method called SIMPLE-M, M means Modified for a collocated grid structure. I do not solve a pressure correction eqn., only the pressure field from the current velocity field. I use the continuity eqn to calculate the velocity on the free surface. I do this every iteration and the convergence is very slow. If I do not include the buoyancy force in the problem the convergence is quick and the solution looks just fine. It is the coupling of the momentum and energy eqns through the buoyancy term that gives me all the trouble. Any suggestions? Any help would be greatly appreciated. Thanks, Chuck