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.

jika

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]

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