# PISO convergence

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 April 28, 2011, 11:05 PISO convergence #1 Member   fisch Join Date: Feb 2010 Posts: 97 Rep Power: 9 Hello, does anybody know if there's a reason for specifying the number of piso iterations/correctors (e.g. using pisoFoam) and not using a convergence criterion for that? If not: Is it possible to specify a criterion to stop the piso iterations if the criterion (e.g. initial residual of the pressure equation is already smaller then the specified one in fvSolution) is reached? Thank you for any advice. rupert

 April 28, 2011, 11:33 #2 Member     David Aljure Join Date: Mar 2011 Location: CTTC Universidad Politécnica de Catalunya. Spain Posts: 38 Rep Power: 8 The way the piso algoritm works is: 1. Predicts the velocity u* using a semi-implicit equation with u*, pn and un. end of predictor step start 1st correction step: 2. Solves a poisson equation for pressure p* using u* and un. 3. solves for u** using u*, p* and un. end of 1st corrector step start 2nd corrector step 4. solves for p** using u** and un. 5. solves for u*** using u**, p** and un. end 2nd corrector step. This are the 2 piso iterations programed by default in pisoFoam, u*** and p** are taken to be close enough to u(n+1) and p(n+1) (see Solution of the implicitly discretised fluid flow equations by operator-splitting R. I. Issa) If you need it, you can do more corrector steps to achieve a better solution (using high order discretizations). In the article Issa demonstrates that the magnitude of the truncation errors in a 2 step piso are of the same order as those introduced by second order discretization schemes, so further iterations are not needed.

 April 29, 2011, 08:06 #3 Member   fisch Join Date: Feb 2010 Posts: 97 Rep Power: 9 Thank you very much. I read the article from Issa. Now it's clear for me (more or less). rupert

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