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Velocity correction and underrelaxation in the SIMPLE algorithm 

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October 15, 2010, 08:25 
Velocity correction and underrelaxation in the SIMPLE algorithm

#1 
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Tobias Elmøe
Join Date: Oct 2010
Location: Denmark
Posts: 9
Rep Power: 8 
Dear all.
Please bear with me as I am a beginner to the field of CFD. My question concerns the update of velocities in the SIMPLE algorithm. Specifically, I am wondering how the update is done when underrelaxation of both momentum and pressure is implemented. In the SIMPLE algorithm the velocity correction comes up by substracting the guessed velocity field with the "correct" velocity field (that satisfies the momentum equation). For the uvelocity in a cubic control volume: substracted from: results in: The correction is then for the velocity and for the pressure. Now as far as I understand it, you discard the sum terms (neighbors). However, after reading Versteegs book, I still do not understand what happens to the underrelaxation term. In Peric, Kessler and Scheurer (1988), Computers & Fluids, 16,4, p. 384403, it seems that the term does not even appear and we're left with: Is this true? Furthermore, what happens to the pressure underrelaxation factor ? Should it be included before the velocity correction equation above? I would be grateful for a clarification Regards Johnhelt 

October 16, 2010, 00:33 

#2 
Senior Member
Hamid Zoka
Join Date: Nov 2009
Posts: 202
Rep Power: 11 
correction is just a rough approximation to conservation equations.
when you apply the SIMPLE algorithm to solve a problem, under relaxation factor will be used to calculate the velocity and it does not make a sence to be applied again in velocity correction step. for example, consider that you have a very complex geometry and you are obliged to use a very small under relaxation factor, say 0.1,. if you apply this factor to momentum equation it will reduce convergence rate considerably but it has no influence on the converged velocity field. but now imagine that you apply 0.1 in the correction step. what will happen? u' or P' will recieve a huge unrealistic change and it may leads in divergence. 

October 18, 2010, 06:27 

#3 
New Member
Tobias Elmøe
Join Date: Oct 2010
Location: Denmark
Posts: 9
Rep Power: 8 
Thank you for the reply, I'm not sure, however, I understand 100%...
You say that introducing underrelaxation may lead to too high velocity change/correction. As I see it, if I have velocity underrelaxation then should decrease with increasing underrelaxation... And, if I then apply the pressure under relaxation factor I get , which then decreases the velocity correction even further. In the end, of course, it should not matter for a converged solution. However, to get there is the key issue :) Regards 

Tags 
relaxation factor, simple algorithm, velocity correction 
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