2D lid-driven cavity flow
 

Hi, I have a problem when simulating a 2D lid-driven cavity flow at Re=100: the velocity profiles at the center lines and the center of the primary vortex match the literature, but the secondary vortices don't. For a lid velocity Ul = +1.0, the vortex located at the right lower corner is smaller than the vortex located at the left lower corner, which could mean that my formulation doesn't obey the momentum conservation. Does anybody knows why this could happen? Also, when I plot the streamlines, they seem to cross the walls when very close to these corners.

Here's my formulation:

>Fractional step for u-v coupling

>1st order - explicit time advance (dt = 1e-4)

>Re = 100

>Simplified viscous term: Dij = d(visc*(dui/dxj))/dxj

>no turbulence modeling

>Finite Element for spatial discretization (quadrilateral elements): 9 node quadratic lagrange element for velocity and 4 node linear element for pressure. The weighting functions are constant and define a control volume around each node (CVFEM). This leads to non-symmetric matrices for the velocity element.

>Lumped mass formulation for the transient term: all the terms in the transient matrix are summed and stored in each row of the matrix. The remaining columns in each row are set to zero.

Re: 2D lid-driven cavity flow
 

How about your nodal spacing? What is the nodal pattern? Are your quads rectangles for the test problem? In other words, how is your flow regime resolved?

I have run this problem (Re = 100) using a finite difference code. The corner vortices at 20 x 20 are much different than those for 40 x 40. Those solutions are for uniform mesh spacing. Going to 50 x 50 with the meshes stretched in the center to allow very close spacing in the corners shows even further change in the corners. For the 40 x 40 and 50 x 50, the centerline velocity profiles match the Ghia, Ghia, and Chin solutions (usually regarded as the standards) very well. I also checked the centerline velocities using CFX - with good agreement also.

These results are in a report you can download from www.ornl.gov. The report number is ORNL/TM-1999/292. The author is James E. Park.

Re: 2D lid-driven cavity flow
 

Hi, Jim. Thanks for your help. My results agree with the report, except for the secondary vortices, and my grid has 71 x 71 points. Before that I had run a case with an unstructured grid even finer at the walls, and the same problem occured. Do you think there could be an error in the spatial discretization or in the fractional step algorithm?

TIA

Márcio Ricardo

Re: 2D lid-driven cavity flow
 

I'm really out of ideas.

The possibility of insufficient resolution was what your results suggested. But I'd think 71 x 71 is enough if the other aspects are OK. By that I mean code correct, time (?) step within stability bounds, etc.

I have no experience with fractional step, or with finite element, so can't help at all there.

Sorry I wasn't of any particular help.

Re: 2D lid-driven cavity flow
 

Thank you, Jim. I'm checking the code for the advective term and the fractional step algorithm.

Thanks for your help

Márcio Ricardo

Re: 2D lid-driven cavity flow
 

Would you please send me the pressure distribution in a cavity flow at low and high Re.

Re: 2D lid-driven cavity flow
 

Re: 2D lid-driven cavity flow
 

Try the following site. There's a lot of information - including papers - about flows in different cavity shapes.

http://www.gyte.edu.tr/enerji/ercane...cavityflow.htm

Re: 2D lid-driven cavity flow
 

Dear Marcio Ricardo,

The address that you have sent, does not have the pressure solution of cavity flow.

Thanks alot