Lid driven cavity
I am working on developing an incompressible flow solver in 2D in a non-staggered framework as proposed in Mahesh et.al. (JCP, 2007). This method stores the Cartesian velocities and pressure at the cell centroids. The pressure is dropped from the momentum equation and a projection step leads to a pressure poisson equation, which is solved using some iterative procedure. While I find this to be working well on cartesian meshes, the same algorithm (which is designed and meant for unstructured meshes) gives non-physical results on traingulated meshes, but only those arising from traingulation of cartesian meshes. On these meshes, the solver does not fail but leads to only one large corner vortex instead of two corner vortices, but these are obesrved on coarser meshes such as a 30*30 cartesian mesh which was traingulated, by joining the diagonals. Triangulating in opposite direction leads to the same problem, surprisingly the position of the corner vortex is reversed. The test case is Re=100 in a [0,1]*[0,1] domain. I am surprised that the algorithm fails only for such kind of grids, and works well with quad meshes, boith cartesian and curvilinear and even for hybrid meshes, provided the right triangulation does not happen at the boundaries. For triangulated Delaunay meshes, no problems are seen. Has anyone encountered such an experience specific to right triangular meshes and driven cavity problem in the past ?
Thanks and Regards,
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