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How to Improve Convergence in Natural Convection

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I am wondering how I can improve convergence in my natural convection model. It is a simple model; an isothermal aluminum plate in water.

The model starts out fine but as the run continues (transient model), the plume begins to lose stability causing the problem to reduce its time stepping. I have tried re-meshing as much as my PC can handle (3 mil elements).
I am wondering what else I can do to solve this problem. Should I change tolerances, crosswind or streamline parameters. I am running out of ideas. Any help would be greatly appreciated ( as I have been stuck on this problem for several days now). I have attached the model (with no mesh or solution). Typically, the model solves the first 20-30 seconds, then the solution becomes very strange and results become unreasonable.

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