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under-relaxation factors -> level of residuals

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under-relaxation factors -> level of residuals

Posted August 27, 2012 at 09:27 by kira

more helpful info on under-relaxation factors:

Originally Posted by LuckyTran View Post
No magic here, that's what's supposed to happen. Unless your solution is diverging, do not bother with the under-relaxation factors. If it is diverging, do as you did, lower the factors until you can a stable solution, and then raise them again if possible. If not, then it is a hint that there is an inherent stability issues in the problem you are trying to solve or perhaps one of your modeling parameters is incorrect.

All your observations are correct. Lowering the under-relaxation factors will limit the change in the solution per iteration, which will make the residuals appear to change less per iteration. Be careful, as this can give a false sense of "oh, my solution is now converged". That is why residuals are not a good measure of solution convergence, they are really only useful for determining if the solution is diverging. Under-relaxation factors does not change the way the solution evolves in the long run, you still arrive at the same solution more or less (unless the solution diverges) it just takes you longer to get there.

As a test (do this as a mental exercise to not waste compute hours), setting all your under-relaxation factors to 0 will make the residuals constant because the solution does not change between iterations. It is possible to obtain very very very small residuals by setting the under-relaxation factors to very small fractions. Again, this does not mean that the solution is converged.

So in general, and this was obvious from the start, you want the highest under-relaxation factors. In fact, over-relaxation (under-relaxation factor greater than 1.0) would be ideal in the sense that you would arrive at the converged solution in the least number of iterations. However, because of the numerical schemes involved there are stability problems, and conservative values for the under-relaxation are necessary to prevent the solution from diverging.
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