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December 31, 2009, 02:21
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Frank
Join Date: Dec 2009
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I’m writing a program to solve the 2D lid-driven problem based on SIMPLE algorithm on a staggered grid using finite-difference method, but cannot get a converged result. My boundary conditions are:
(1) u=0 and v=0 at 3 walls; u=0.5 m/sec, v=0 at the lid;
(2) dp/dn=0 (i.e. p[boundary]=p[inside_neighbor]) at all 4 sides;
(3) p’=0 at all 4 sides.

The attached picture shows a screen capture of the velocity (u) distribution. Red color represents the highest velocity (to the right). Blue color represents the lowest.

The simulation blows out after about 190 iterations. It seems the problem starts at the rightmost point of the lid, where the flow shall make a turn (from +x direction to –y direction).

Can someone tell me what went wrong with my program? Or are there any special techniques (or boundary conditions) to treat singularity points like this?

Thank you!
Attached Images
 u.png (10.3 KB, 56 views)

 December 31, 2009, 10:05 #2 Member   private Join Date: Mar 2009 Posts: 74 Rep Power: 16 You've left out a lot of detail. 1. What relaxation factors are you using? Too large and the iterations will diverge. You might try systematically reducing your factors to see if you can get convergence. 2. With a staggered grid, the corner 'singularities' are not a factor - you never need to assign values for the velocities or pressures at the corners. 3. Are you using the Rhie-Chow technique for switching from cell centers to cell edges (and back) during each iteration? I haven't worked with SIMPLE, but I have solved the driven cavity with the LANL Sola codes. And before that, the SMAC algorithm. These both use time marching (with fixed rules for allowable time step size) as a form of relaxation. Perhaps someone who's worked with SIMPLE can help.

 January 10, 2010, 13:54 #3 New Member   senthil Join Date: Jan 2010 Location: lincoln Posts: 1 Rep Power: 0 hi, There is no enough information to say where the error would be. Staggered is a bit tricky to start with. I have decent experience with staggered grid. Perhaps, I can help debugging. I don't have any reservation in sharing parts of my 2d code even. Senthil

 January 12, 2010, 12:03 Thank you otd and senthil #4 New Member   Frank Join Date: Dec 2009 Posts: 2 Rep Power: 0 Thank you otd and senthil for offering help! But I found the problem in my code. There was an error in handling the boundary conditions! BTW, do you think collocated grid is superior than staggered grid? Is it difficult to program with collocated grid on 3D complex shapes? Thank you!

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