Method for solving the adjoint equations
I have run several cases and found it difficult to obtain a converged
solution of the adjoint N-S equations. I think it is related to the adjoint
transpose convection term. I use the SIMPLE algorithm to couple the
adjoint velocity and pressure.
What should I do to improve convergence of the adjoint equations?
Any information, however small, would be appreciated.
First, check that you should get a solution that converges. For high Re, (even about 40 in some cases), you would get a time-dependent solution. To check that it works for low Re, increase the viscosity, decrease the velocity, etc. If this doesn't work, there is a problem.
I don't know much about the SIMPLE algorithm, but if it involves solving a system of equations, try using a pre-conditioner. Without a pre-conditioner, I was not able to get a good result quickly. I implemented the gauss-siedel conditioner and it works like a charm. (Though maybe I should use SSOR!)
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