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April 20, 2004, 08:41 
transient run and residuals

#1 
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Hi,
could someone shed some light on the use of residuals during a transient run. 1. How can I estimate in advance at which residual level a time step can be considered as converged? Sometimes it happens that at the beginning the level of e.g. 10e5 is reached after 20 outer iterations. After a while only 2 outer iterations are needed to fall below the limit. 2.Can I still expect a valid result even if there where only 2 iterations per time step? Cheers, Mark 

April 20, 2004, 13:10 
Re: transient run and residuals

#2 
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I think that if you are correctly computing your residual and you get a sufficiently small value then you can call that convergence, no matter how many iterations it took.


April 21, 2004, 08:07 
Re: transient run and residuals

#3 
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not sure if i get what you mean. you have converged if your residuals change no more. and what is called residual in transient case is ambiguous, could be norm could be e.g. biggest change. if by outer iterations you mean momentum iterations then im not sure again what you ask  in my case often few pressure corrections (inner iterations) suffice.


April 21, 2004, 09:19 
Re: transient run and residuals

#4 
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Compute with your grid and twice thinner grid until you reach some precisity  your (1e5) or smaller. If your scheme has a good approximation row of error the thinner grid will be closer to the solution. So take the difference between the two grids at the common points and multiplied by 1.5 (in case of O(h2)  approximation error) or 2 (in case of O(h)), this will be your precisity of calculations that can be practically reached. Calculating after reaching this precisity with the original grid will not give you more precise result.
I'm not sure but you can try something else: Calculate until the differences of the two grids in the common points become less than some value. I'll be glad to know what happened if you decide to apply one of these suggestions. Mihail 

April 21, 2004, 10:12 
Re: transient run and residuals

#5 
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>>could someone shed some light on the use of residuals during a transient run.
>>1. How can I estimate in advance at which residual level a time step can be considered as converged? I cannot give a conclusive answer for this, but it is not different from a stationary solution in this respect. >> Sometimes it happens that at the beginning the level of e.g. 10e5 is reached after 20 outer iterations. After a while only 2 outer iterations are needed to fall below the limit. >> 2.Can I still expect a valid result even if there where only 2 iterations per time step? It is reasonable that the later timesteps need less iterations to converge, since their initial conditions are the converged solution of the former step, which should be quite close (unless the timestep is too large). Moreover, as the solution changes become smaller (which is usual in many problems, even if steady state is not reached), this is more likely to be the case. 

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