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Solution instability in meshes containing small cells.

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Old   July 16, 2015, 11:07
Default Solution instability in meshes containing small cells.
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Hi all,

Iíve run into a problem that seems to arise from cells in meshes that contain cells that are of the order of 10^-6 m in size or less. The problem manifests itself as a rapid increase in Courant number leading to ultimate divergence of the solution.
It should be noted that in all the cases, the time step that would one calculate from the CFL condition leads to a divergence in the solution as well. In fact a time step of nearly 3 orders of magnitude smaller than the calculated time step is required to achieve a steady solution.
Although I have attached cases involving only 2 solvers, icoFoam and pimpleFoam, the cases have also been tested with simpleFoam and pisoFoam.
The problem is independent of the p and U solvers and has been replicated across multiple solvers.
To demonstrate the problem I have included 3 test cases. The first two are the well-known cavity and pitzDaily cases, the last one is a simple square duct.
This case has been duplicated across multiple geometries and is dependent only on mesh size. It is worth noting that these cases run satisfactorily on larger time steps as soon as the mesh size is increased.
I have also included the links to the zipped folder containing the 3 cases. Each case folder also includes an animation scene of the development of the Courant number with time.

Have there been any previously documented cases involving poor stability due to very small length scales in the mesh?

Attached Files
File Type: txt cavity_log.txt (27.1 KB, 0 views)
File Type: txt pitzDaily_log.txt (44.0 KB, 0 views)
File Type: txt blockMeshDict_pitzDaily.txt (4.0 KB, 0 views)
File Type: txt square_cavity_log.txt (9.2 KB, 0 views)
File Type: txt blockMeshDict_square_duct.txt (24.4 KB, 0 views)
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