Towards Time-Stable and Accurate LES on Unstructured Grids
Control-volume (cv) and node-based (cell-vertex) finite volume discretizations of the incompressible Navier-Stokes equations are compared in terms of accuracy, efficiency, and stability using the inviscid Taylor vortex problem. An energy estimate is shown to exist for both formulations, and stable convective boundary conditions are formulated using the simultaneous approximation term (SAT) method. Numerical experiments show the node-based formulation to be generally superior on both structured Cartesian and unstructured triangular grids, displaying consistent error levels and nearly second-order rates of L 2 velocity error reduction. The cv-formulation, however, out-performs the node-based for the case of Cartesian grids when the Taylor vortices do not cut the boundary.
KeywordsDirichlet Boundary Condition Energy Estimate Unstructured Grid Unstructured Mesh Cartesian Grid
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