# SIMPLE for compressible flows

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 August 16, 2005, 08:34 SIMPLE for compressible flows #1 Luuk Guest   Posts: n/a Hello, I need some help with the following. I'm implementing the SIMPLE method for compressible flow calculations in an incompressible finite volume code. I'm following the approach described by Ferziger and Peric in Computational Methods for Fluid Dynamics. I'm a bit confused by the following: I have 3 variables: pressure (p), density (rho) and temperature (T). I solve a transport equation for T, so it is known. In the SIMPLE method, I calculate a pressure correction (p') and a density correction (rho'). To calculate the (new) p and rho, I have 3 possible equations: equation of state (p=rho*R*T), p_new=p+p' and rho_new= rho+rho'. Summarizing: Option 1: p_new=p+p' and rho_new=rho+rho' ; Option 2: p_new=p+p' and rho=p_new/RT ; Option 3: rho_new=rho+rho' and p=rho_new*R*T. What is now the best option (in terms of stability and accuracy)? Thanks in advance for any help, Luuk

 August 16, 2005, 08:55 Re: SIMPLE for compressible flows #2 ag Guest   Posts: n/a In my (limited) experience I have found option 2 to be the most robust.

 August 20, 2005, 08:45 Re: SIMPLE for compressible flows #3 George Guest   Posts: n/a Hi Luuk! I have exactly the same question. I have tried the 3 options and I get very different convergence rates. Also the results that I get are better with the first option, while with the second option are very strange, although I agree with Ag that the second option looks more robust. I am on holidays at the moment and I hope when I return to discuss this matter again. Bye

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