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Under-relaxation factor and residuals

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Old   July 27, 2010, 20:34
Default Under-relaxation factor and residuals
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I've seen posts regarding this but I'm still not sure how to solve it.

I've got a 1-D code that uses SIMPLER algorithm. I'm trying to study flame propagation using it.

The problem is I get different results when I change the under-relaxation factor (URF). I did a simple test case with pure diffusion, with velocities set to zero and observed the same thing, i.e. my results only agreed with the closed-form solution only when I set URF to unity.

After reading the posts, I've realised that the problem might be because of how the convergence criteria was defined. At the moment the error is evaluated using the 2-norm of the residual:

||error||_2 =\left( \sum_{i=1}^N\, |x-x_{old}|^2 \right)^{1/2}

What other criteria can I use to check for convergence (for example, assuming that it's just a simple diffusion?)

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