2D lid-driven cavity using SIMPLE algorithm convergence

Moreza7 · July 5, 2019, 10:02

Hi,
I wrote a MATLAB code for 2D lid-driven cavity using SIMPLE algorithm. (Central Method)
(Using Versteeg Book formulation)

The problem is, that it only converges at relaxation factors of smaller than 0.001 for pressure equation. However, the solution seems to be OK.

Is that OK to have such a small under-relaxation factor?

spelletier · July 8, 2019, 02:08

I am curious as to what someone far more experienced then me will say so take the following with a grain of salt. I`m also a fluet user not a matlab user.

The under relaxation factors control the convergence and stability by scaling the impact of the calculated value. Essentially:

Xn+1 = Xn*underelaxation + (1-underelaxation)(Xn-1)

So by decreasing the underelaxation you would be increasing the convergence time although at .001 it would seem like you are basically not taking into account pressure unless you are doing a very high number of iterations.

FMDenaro · July 8, 2019, 03:50

To understand the general role of such factors in the convergence of an iterative method I suggest to start back from the theory of stationary iterative methods for linear algebric system. You will see that the introduction of such a factor enters into the iteration matrix. The value changes the spectral radius of the iteration matrix so that you can get acceleration if the spectral radius is lesser than the original one and a deceleration for a greater value. And using wrong values you can get also that the process is no longer converging.

Moreza7 · July 8, 2019, 05:18

Thank you all.
I just noticed that one of my loops was incorrect.
Now it's working with U.R of 0.3.

Fluidentity13 · November 9, 2021, 01:07

Quote:

Originally Posted by Moreza7

Thank you all.
I just noticed that one of my loops was incorrect.
Now it's working with U.R of 0.3.

Hi,

Can you please elaborate on the mistake. I've been stuck on this for days on end (UPWIND Scheme) with multiple types of grid & boundary treatment. Same issue, solution blows up for U.R.F Pressure above 0.01.

Moreza7 · November 10, 2021, 05:06

Quote:

Originally Posted by Fluidentity13

Hi,

Can you please elaborate on the mistake. I've been stuck on this for days on end (UPWIND Scheme) with multiple types of grid & boundary treatment. Same issue, solution blows up for U.R.F Pressure above 0.01.

Hello, I really don't remember what the problem was!
But I can send you my code. If you'd like, you can send me your Email address.

Fluidentity13 · November 10, 2021, 09:10

Quote:

Originally Posted by Moreza7

Hello, I really don't remember what the problem was!
But I can send you my code. If you'd like, you can send me your Email address.

That'd be great. Thanks a lot.

aman.sangal13@gmail.com

July 5, 2019, 10:02	2D lid-driven cavity using SIMPLE algorithm convergence	#1
Moreza7 Senior Member Join Date: Jan 2018 Posts: 121 Rep Power: 8	Hi, I wrote a MATLAB code for 2D lid-driven cavity using SIMPLE algorithm. (Central Method) (Using Versteeg Book formulation) The problem is, that it only converges at relaxation factors of smaller than 0.001 for pressure equation. However, the solution seems to be OK. Is that OK to have such a small under-relaxation factor? Last edited by Moreza7; July 5, 2019 at 20:20.

July 8, 2019, 02:08		#2
spelletier New Member Sebastian Pelletier Join Date: May 2019 Posts: 12 Rep Power: 6	I am curious as to what someone far more experienced then me will say so take the following with a grain of salt. I`m also a fluet user not a matlab user. The under relaxation factors control the convergence and stability by scaling the impact of the calculated value. Essentially: Xn+1 = Xn*underelaxation + (1-underelaxation)(Xn-1) So by decreasing the underelaxation you would be increasing the convergence time although at .001 it would seem like you are basically not taking into account pressure unless you are doing a very high number of iterations. Moreza7 likes this.

July 8, 2019, 03:50		#3
FMDenaro Senior Member Filippo Maria Denaro Join Date: Jul 2010 Posts: 6,764 Rep Power: 71	To understand the general role of such factors in the convergence of an iterative method I suggest to start back from the theory of stationary iterative methods for linear algebric system. You will see that the introduction of such a factor enters into the iteration matrix. The value changes the spectral radius of the iteration matrix so that you can get acceleration if the spectral radius is lesser than the original one and a deceleration for a greater value. And using wrong values you can get also that the process is no longer converging. Moreza7 and Fluidentity13 like this.

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July 8, 2019, 05:18		#4
Moreza7 Senior Member Join Date: Jan 2018 Posts: 121 Rep Power: 8	Thank you all. I just noticed that one of my loops was incorrect. Now it's working with U.R of 0.3.