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Under Relaxation factors in a transient solution

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Old   October 7, 2014, 19:44
Default Under Relaxation factors in a transient solution
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Joshua Brickel
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I have a question on how Star-CCM+ handles transients solutions when using an under relaxation term.

Traditionally I have done steady state solutions, so the under relaxation terms helped out with convergence. That is u(i+1) = u(i) + R*(u'(i+1) -u(i))

where;
i= iteration
R = Relaxation factor
u = field function be solved for

So for a steady state solution this simply slows down the convergence which can be useful if otherwise the solution will diverge before a proper solution can be found.

However now turning to transient cases....

now "i" is the time step, and thus the relaxation factor while maybe preventing divergence also causes the wrong value to be determined at i+1. If for instance R = 0.5 it is almost like saying you solved for u'(i+1) for time step i, but we will only set it to something between that and u(i). Since we need convergence at each step, this would seem a wrong approach....

I must have something wrong here, can anyone fill me in.

thanks,

Joshua
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Old   October 8, 2014, 05:55
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David
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here "i" should be inner iteration for unsteady case.
You can regard a steady case as a single time step in unsteady case.
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Old   October 8, 2014, 16:02
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Joshua Brickel
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Hi David,

Yep, thanks, that answered the question.

Once I looked into it I realized that the default maximum "inner iterations" was way too low. Hence the solution at each time step was never even getting closer to convergence before the solver was forced on to the next time step.
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transient convergence, under-relaxation factor, unsteady flow

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