Method for solving the adjoint equations

fumiya · June 12, 2011, 22:31

Hi,

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.

Best regards,
fumiya

Petrov · June 13, 2011, 01:18

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!)

Good luck!

June 12, 2011, 22:31	Method for solving the adjoint equations	#1
fumiya Senior Member Fumiya Nozaki Join Date: Jun 2010 Location: Yokohama, Japan Posts: 266 Blog Entries: 1 Rep Power: 19	Hi, 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. Best regards, fumiya

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June 13, 2011, 01:18		#2
Petrov New Member Felipe Hernandez Join Date: Apr 2011 Posts: 13 Rep Power: 15	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!) Good luck!