hydrodynamics
I am simulating a driven cavity case with the upper lid moving towards right side while the bottom lid moving left. I supposed that there must be exact symmetrical and the result for low Reynolds showed this. But when Re goes higher, these are obvious insymmetrical flow patterns. I try every means to deal with this but I failed. Then I think it may be cause by hydrodynamic instability and the insymmetrical is physical. I am not sure of this. I would appriciate any explainations. Many thanks.
Zhou 
Re: hydrodynamics
(1). It's hard to answer your question, because you did not state the essential information, such as the Reynolds number, the total mesh size and distribution, the numerical method used. (2). Some numerical methods are not stable and will produce oscillations when Reynolds number increases. (3). You can try the conventional "upwind" method and check your results again. It should be stable enough. (it might not be the most accurate method) (4). Once you have the solution, you can refine your mesh and improve your solution accuracy. (5). So, the suggestion is: refine your mesh and use upwind method. also try to use the steadystate method to see whether the solution is still oscillating or asymmetric.

Re: hydrodynamics
You may find the following paper useful:
"Multiplicity of Steady TwoDimensional Flows in TwoSided LidDriven Cavities" by S. Albensoeder, H. C. Kuhlmann, and H. J. Rath, Theoret. Comput. Fluid Dynamics, vol. 14 (2001), pp. 223241. 
Re: hydrodynamics
Thank you very much! :)

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