Strange Result for Versteeg Testcase (2D, convection only, steady state)
Hi everybody,
I'm new to OpenFOAM and tried to implement a testcase from the Versteeg and Malalasekera book[1]. GoogleBooks To solve the problem I used the scalarTransportFoam solver and set DT = 0 as it is a convection only problem. I used the boundary condition from the book except for the two outlet patches, where I used zeroGradient for phi. The result I get are quite normal as long as I don't reach a certain number of cells. For example if my domain is 1 x 1 m and I use more than 21 cells in the x_1 and the x_2 direction the result is completely instable and has nothing to do with the analytic solution. I solved the div(phi,T) term with Gauss linear. But the solution doesn't converge either if I use QUICK or vanLeer to compute the gradient. Only upwind always give a reasonable but not really accurate solution. Does anybody have an idea what problem is? Thanks in advance. caramelo 
Can you post an sketch of the problem and BC's used?
Regards. 
1 Attachment(s)
You can see a sketch in the GoogleBooks links i posted. I just added the whole case as an attachment. With this setting you will get a reasonable result. If you now increase the numbers of cells in the blockMeshDict, no reasonable result will be received any more.

When you get finer grid cells, I think there's an issue with the Courant number for nonupwind schemes. Try changing ddtSchemes to Euler and make the endTime in controlDict something like 2; I get 'better' results with that.
I note that: "At the first and last nodes where the diagonal intersects the boundary a value of 50 is assigned to \phi." Might that be an issue? 
It is simply a question of conditioning of the linear problem you are trying to solve. You would need underrelaxation (have to modified the code adding T.relax()) to use the code as steady state.
Alternatively, simply perform a pseudotransient simulation, as suggested by Laurence, since the effect is the same as underrelaxing. P.S. It is not a problem in the schemes ;) Best, 
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