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April 24, 2020, 11:12 
Lid Driven Cavity (SIMPLE)

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Hello, I am trying to code the lid driven cavity problem using SIMPLE method and FVM discretization with staggered grid and ghost cells.
Steps followed 1. Found the velocity coefficient matrix for u,v (incorporated the BC in the coefficient matrix for corner and boundary cell) 2. Found the updated velocities using momentum equation 3. Found the coefficient matrix for pressure correction (incorporated the BC in the coefficient matrix for corner and boundary cell) 4. updated p,u,v Central differencing scheme used to discretize. I am facing some issues in the results for centerline velocity. Thanks in advance 

April 24, 2020, 12:01 

#2  
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Filippo Maria Denaro
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What is the problem? Why do you think to get exactly the same results obtained by Fluent? 

April 24, 2020, 12:08 

#3 
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I am not looking for the exact results but I'm concerned about the curvature it achieves after reaching the minima. That curvature increases as I decrease the grid spacing and hence the error.


April 24, 2020, 12:13 

#4 
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Filippo Maria Denaro
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I suggest to compare to the well known results in literature (for example Ghia & Ghia) using the same Re and a similar grid.
Check both velocity profiles in the centerline and the recirculation region. Check if the divergencefree constraint is satisfied. 

April 24, 2020, 12:51 

#5 
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Yes, the divergence free condition is satisfied. I've posted the comparison for Ghia et al. Probably this would give you a better picture


April 24, 2020, 12:55 

#6  
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What about the Re number? What about the comparison to the other velocity component? Plot the streamlines and check that your solution achieved a convergent result. 

April 24, 2020, 13:35 

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The Re is 100. V velocity is actually worse


April 24, 2020, 13:39 

#8 
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April 24, 2020, 13:43 

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If the successive change in velocity is less than 1e6, it stop the solution. The grid size is 31x31 which is quite decent. The other results from similar mesh seem to have got a pretty accurate result.


April 24, 2020, 14:10 

#10  
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Filippo Maria Denaro
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That makes no sense in terms of convergence, you have to monitor the residuals 

April 24, 2020, 14:23 

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Also, keep in mind that am monitoring residuals from continuity equation. 

April 24, 2020, 14:29 

#12  
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Filippo Maria Denaro
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Not at all, the differences between old and new values are not the residuals of the equations. A.x^kq=r^k is the kth residual 

April 26, 2020, 08:52 

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April 26, 2020, 11:25 

#14 
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Filippo Maria Denaro
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April 26, 2020, 11:41 

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No it does not diverge. To me it seems that either something is wrong with the link coefficients for u,v in momentum equation as I incorporate the boundary conditions. The interior nodes look good to me. Or there could be something wrong in the way I am implementing relaxation factors.


April 26, 2020, 12:00 

#16  
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Quote:
what do you mean? the norm on the u and v residual become constant? 

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