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August 13, 2012, 04:56 
about under relaxation factor

#1 
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B Aram
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I have a question about setting under relaxation factor.
is changing the relaxation factor supposed to change the final answer?! when i changed it in a problem, the final solution that i was expected wasn't gained and when i decreased it again, the final solution changed again 

August 13, 2012, 06:25 

#2 
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Alex
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If your "final" solution is obtained based on a residuum, not on a number of iterations, then the results should be independent of the underrelaxation factor.


August 13, 2012, 09:02 

#3 
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Jonas T. Holdeman, Jr.
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Yes it should, but this is not always the case. When the sequence of residuals is not monotonicly decreasing, it may not converge without relaxation. What is happening with relaxed convergence is that the advection velocity, i.e. Ubar in the expression (Ubar dot grad U), is implicitly filtered or smoothed, averaged over many iterrations. So what you get is not necessarily the solution to the original NS equation (which may not exist), but is the solution to a smoothed advectiondiffusion equation. This will be the same as the solution to the unrelaxed equation where the latter exists (Ubar=U), but can provide a generalized solution when it doesn't.
Last edited by Jonas Holdeman; August 13, 2012 at 09:04. Reason: grammar 

August 13, 2012, 11:51 

#4  
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Quote:
With an improper value of relaxation factor your solution can blow up. with a good one the solution will converge. But there are plenty values for which the solution will converge. For all theses values the solution should be the same (especially for steady cases) and the only difference will be the rate of convergence. As an example it is often recommended to underlax the pressure for incompressible flow. Underlaxation factor over 0.7 may blow up your code,it is really problem dependent. For UF =0.6 it may converge, but for UF=0.5 also and for UF=0.2 too. For all theses values between 0.2 and 0.6 you will obtain the same solution. But there is an optimal value for which your code will converge faster. Generally it is the highest value for which the code still converge just over this limit it diverges. Some authors have prescribed that UF_velocity+ UF_p = 1 

August 14, 2012, 03:14 

#5 
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thanks for your considerations
my problem is a simple steady state problem that is devised just for evaluating the effect of under relaxation factor on convergance. the physics of problem indicates that the solutuion should be a linear gradient for temperature. it is true for URF = 1 but when the URF is decreased, it's no longer linear. although decreasing the factor has a positive effect on convergance. 

August 14, 2012, 04:24 

#6 
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So I'm afraid there is a bugg in your program in the way you implemented the URF.


August 14, 2012, 04:33 

#7 
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ok thanks alot


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