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jika June 19, 2002 07:41

SIMPLE algorithm
Hello Sirs,

I am a beginner of cfd. I am trying to solve steady, incompressible, laminar, 2D driven-cavity flow problem using SIMPLE algorithm. As I have to use pressure relaxation factor of 0.001 to get a converged solution at Reynolds Number = 100 and as I am not getting convergence for Reynolds number > 200 at this pressure relaxation factor also, I want to ask the following questions -

1)In momentum equations,

(a_P) = (summation of a_nb) + (flux difference over the cv)

this relation maynot give a diagonally dominant matrix when the solution is not converged. So I am using

(a_P) = (summation of a_nb) + MAX[0,(flux difference over the cv)]

in my program. Is it correct?

2)How to use time-stepping in this problem? How to deal with the term

(rho_p^o - rho_p).Delta V / Delta t

which arises in the transient pressure correction equation?

My 100 Re result is matching very well with benchmark solution. I have tested different grid sizes (uniform) from 10x10 to 100x100. I am using upwind scheme for covective terms.

I have read the previous discussions on SIMPLE algorithm here. I have gone through the books by Peric, Patankar, Malalasekera. But still I am not clear on these points. Where I may be wrong? Please help me.

Thanking you in anticipation.


arash July 3, 2002 12:50

Re: SIMPLE algorithm
hi jika I had some problem like you but about 1 think That's not correct.flux difference over the cv has a physical meaning and you can not delet it in some equation. about 2 there is a code that Peric developed it. you can get it and compare your code with it .you can learn many things about SIMPLE algorithm in those codes.

mhm October 22, 2009 06:46

I suggest you to studying chapter 6 of An Introduction to Computational Fluid Dynamics - Versteeg.
It is very good.

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