Regarding optimizing the underrelaxation factor
Dear friends, I have developed a code for solving flows in 2d geometries ( on BFC grid) based on SIMPLER as proposed by KC Karki( Karki and Patankar, 1988 , Numerical Heat Transfer). I want to optimize the underrelaxation factor as it is very time consuming otherwise. Can somebody tell me how to do it? Or is it just trial and error all the way ?

Re: Regarding optimizing the underrelaxation fact
I suggest using the Simplec algorithm from Doormal and Raithby. It doesn't need any relaxation factor to optimized. See:
J. Doormal and G. Raithby, Enhancements of the SIMPLE algorithm for predicting incompressible fluid flows. Numerical Heat Transfer part B, 7:147163. 1984. 
Re: Regarding optimizing the underrelaxation fact
I suggest that you use Automatic Differentiation to do that. There's a report that may help also: Paul Hovland and Michael Heath. "Adaptive SOR: A Case Study in Automatic Differentiation of Algorithm Parameters," Technical Report ANL/MCSP6730797, Mathematics and Computer Science Division, Argonne National Laboratory, 9700 S. Cass Ave., Argonne, IL 60439, 1997. zaid

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