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Old   August 18, 2011, 15:18
Default Very small residual
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Orxan Shibliyev
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Hi everyone!

For common residual definition which is,

r = b - A*y

I get a very small value even at the beginning (about e-5). So I'm not sure how I can set a criterion of convergence.

Waiting your precious answers.
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Old   August 18, 2011, 16:07
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Ertan Karaismail
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One option could be using normalized value for setting convergence criterion;

Rn_i=R_i/R_1 < tolerance

where,

Rn_i= normalized residual from the ith iteration
R_i = residual from the ith iteration
R_1= residual from the 1st iteration (generally max residual)
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Old   August 18, 2011, 16:37
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Orxan Shibliyev
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Mr. Ertan

Thank you. But in this case what should be the proper tolerance? How can I be sure that, chosen tolerance is enough for accurate results?
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Old   August 18, 2011, 17:03
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Quote:
Originally Posted by orxan.shibli View Post
Mr. Ertan

Thank you. But in this case what should be the proper tolerance? How can I be sure that, chosen tolerance is enough for accurate results?
you would need to check at the history of some physical quantities of the flow plotted vs the number of iteration. for example lift, drag, heat transfer, etc...
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Old   August 19, 2011, 11:40
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That depends on how much accuracy you need. For unsteady flows, it should be safe to can pick a tolerance (convergence criterion) of 0.001 or less for the normalized residuals. For steady flows, I would suggest setting the convergence criterion to a very low value, such as 10^-10. This way you could minimize the iteration error in your calculations. (If you plot residuals, you should be able to see them level off (flatten) after a while).

HTH
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