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Why Relaxation factor (URF) for presure in SIMPLEC is set to 1?

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Old   June 19, 2021, 03:28
Default Why Relaxation factor (URF) for presure in SIMPLEC is set to 1?
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Mandeep Shetty
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Why is the URF for pressure term, when using SIMPLEC algorithm, is usually set as 1? i.e.Why doesn't the pressure term require under relaxation? Why is it not recommended to change it from its default value? (There is no such recommendation when using the SIMPLE algorithm.)
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Old   June 19, 2021, 04:55
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It is very well illustrated in the new edition of the Ferziger et al. book. Basically, the reasoning can be split in two parts:

1) All these methods (SIMPLE, SIMPLEC, PISO, etc.) involve a velocity correction (the term that actually links velocity and pressure) proportional 1/(Ad+Ad*) where Ad is the matrix coefficient on the diagonal and Ad* is the sum over the coefficients of the neighbors. Now, Ad+Ad* might be 0, so here arises the need for velocity under-relaxation, which would make Ad+Ad*>0 no matter what.

2) Now, the main difference between SIMPLE and SIMPLEC is that the former actually has Ad* = 0. So the pressure correction from SIMPLE is proportional to 1/Ad while the one from SIMPLEC is proportional to 1/(Ad+Ad*). As Ad* actually cancels out some or all of Ad, turns out that the amount of pressure correction needed for SIMPLEC is much smaller than what needed from SIMPLE to produce the same velocity correction. So, the latter needs to have the pressure correction reduced with respect to SIMPLEC. Actually, one can show that the pressure relaxation factor to be used in SIMPLE that would match the SIMPLEC behavior is \alpha_p=1-\alpha_u.

So, while this is not, I think, a proper demonstration of why it is needed in SIMPLE, it is quite close to. It is not needed in SIMPLEC (for orthogonal grids) and SIMPLE is made like SIMPLEC by using the value above.
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simplec, under relaxation factor, urfs

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