Can we solve directly Stokes equations?

[thelight · April 3, 2010, 17:12

Hi everyone.
Since the steady (2D) Stokes equations are linear, I have formed a matrix for both U, V and P and solved directly. The staggered grid was used. To avoid the case of singular matrix, pressure is fixed at a given point by add one more row(with only one non-zero element) to the matrix(so the matrix is non-square but still can solve)

I used this method to solve for a simple cavity problem with Utop = Uo.
When Uo = constant, I can get a good result.
But if Uo is changed along the top edge (Uo = Uo(x)) the result looks terrible!

Could you please give me any comments on the method I have used?
If my method is acceptable, please give me some suggestions to deal with the case of Uo = Uo(x).
Thank you very much.
Best,
The

[thelight · April 4, 2010, 15:06

Hey friends, where are you? Could you let me know your comments, anything is also good to me.
Thanks alot!

April 3, 2010, 17:12	Can we solve directly Stokes equations?	#1
[thelight New Member the Join Date: Jan 2010 Posts: 2 Rep Power: 0	Hi everyone. Since the steady (2D) Stokes equations are linear, I have formed a matrix for both U, V and P and solved directly. The staggered grid was used. To avoid the case of singular matrix, pressure is fixed at a given point by add one more row(with only one non-zero element) to the matrix(so the matrix is non-square but still can solve) I used this method to solve for a simple cavity problem with Utop = Uo. When Uo = constant, I can get a good result. But if Uo is changed along the top edge (Uo = Uo(x)) the result looks terrible! Could you please give me any comments on the method I have used? If my method is acceptable, please give me some suggestions to deal with the case of Uo = Uo(x). Thank you very much. Best, The Last edited by [thelight; April 3, 2010 at 17:33.

Similar Threads
Thread	Thread Starter	Forum	Replies	Last Post
Navier Stokes equations in rotation frame..?	vinayender	Main CFD Forum	2	December 1, 2009 00:12
the Stokes and Brinkman equations	yang	Main CFD Forum	4	January 18, 2006 06:20
Stokes algorithm?	Rui	Main CFD Forum	1	March 17, 2003 13:14
Computational complexity of Navier Stokes equations	Marco Ellero	Main CFD Forum	5	May 5, 1999 21:07
pouring a liquid	Ray Roberts	Main CFD Forum	6	February 5, 1999 14:07

April 4, 2010, 15:06		#2
[thelight New Member the Join Date: Jan 2010 Posts: 2 Rep Power: 0	Hey friends, where are you? Could you let me know your comments, anything is also good to me. Thanks alot!