We are trying to model a high reynolds number (Re> 100,000) incompresible flow problem which is lid driven, like the cavity flow, and completely enclosed, but the lid is steeply curved into the cavity. We have been trying to use a mixed interpolation finite element solution, without upwinding, but even when stepping up the reynolds number we are having trouble getting passed Re=10,000. We also have a (k-l) turbulence model in the code and when applied to the standard problems with an inlet and outlet we seem to be able to reach high reynolds numbers (>100,000). It appears that the fixities in corners where the lid and walls intersect are strongly related to the problem. Other researchers that have looked at this particular problem have used SIMPLE or SIMPLER, and have achieved the desired Reynolds number by stepping up to it, on suprisingly coarse meshes, and have made no mention of any special treatment of corner boundary conditions. Why is the SIMPLE procedure able to handle this problem, and is the only way to use mixed interpolation to go to upwinding?

There might be more than of cause of your troubles:

1) velocity-pressure coupling : your are using FEM, are you sure that the interpolation functions are adequate (you should'nt use the same interpolation for functions for pressure and velocity unless you use some "penality functions") For FVM or FDM we mostly you use staggered grids to implicitly introduce different interpolation functions for pressure and velocity;

2) SIMPLE or SIMPLER are only algorithms, personaly, I prefer SIMPLEC or projection's schemes since thay do not involve any relaxations parameters.

3) For High Re numbers, upwinding (SUPG methods), artificial viscosity or flux limiters is manditory to avoid unwanted oscillations in the solutions. I fyou don't do so, It can be easily prooved that "wiggles" will appeared if the local Re (Peclet) number is higher than 2.

We are using quadratic interpolation for the velocity and linear velocity for the pressure, thus the elements satisfy the Brezzi-Babuska condition in FEM and avoid chequerboarding.

I think we will either try some form of penalty function method (as they seem to be in fashion at the momment in FEM!) or CVS-type method, but I have only seen this method applied to transient, not steady-state. Thanks for your response,

Nick

Hi there,

I tried the cavity flows with the finite element method. I used the equal-order approximations for both velocity and pressure (fractional projection, pressure conditionally stabilized). Without upwinding, I computed the results up to Re=10,000. With relatively lower resolutions, the results are identical to those by Ghia¡¯s et al. I did stepped up the Re and averaged the corner velocity. But I am not sure if they played an important role. You may try the TVD in time. It is simple and efficient, to my experience.

Hope this helps.

Tony