Regarding optimizing the under-relaxation factor
 

Dear friends, I have developed a code for solving flows in 2-d geometries ( on BFC grid) based on SIMPLER as proposed by KC Karki( Karki and Patankar, 1988 , Numerical Heat Transfer). I want to optimize the under-relaxation 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 under-relaxation 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, 7:147-163. 1984.

Re: Regarding optimizing the under-relaxation 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/MCS-P673-0797, Mathematics and Computer Science Division, Argonne National Laboratory, 9700 S. Cass Ave., Argonne, IL 60439, 1997. zaid