TVD scheme in unstructured finite volume discretization
I am trying to extend the TVD scheme to an unstructured finite volume discretization. The problem is determining r for this scheme in the unstructured mesh domain, which is defined as the local ratio of upstream gradient to downstream gradient (from Coputational Fluid Dynamics: The FVM by Versteeg and Malalasekera). Any help with this would be greatly appreciated.
Thanks in advance.
Although not directly relevant to your question, please take a look at Jasak's paper on developing higher order NVD schemes for unstructured meshes. These are related to TVD, and the paper talks about developing Gamma scheme, which wroks fine for a range of problems on arbitrary polgonal meshes. You can google the paper, I don't recall the exact title.
Now I'm reading 'TVD schemes for unstructred grids', M.S.Darwish, Int. J of Heat and mass transfer, 2003, 599-611
I just leave this message for someone else...
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