Entropy conservative and entropy stable finite volume schemes for multi-dimensional conservation laws on unstructured meshes
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2012-10
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Report
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Abstract
We present entropy stable schemes for the two-dimensional Euler equations on unstructured grids. We develop a novel energy conservative scheme that is very simple to implement, is computationally cheap and is stable compared to other existing energy conservative schemes. To allow for a correct dissipation of energy in the vicinity of shocks, a novel numerical diffusion operator of the Roe type is designed. The energy conservative scheme, together with this diffusion operator, gives an energy stable scheme for Euler equation on unstructured grids. Numerical experiments are presented to demonstrate the robustness of the proposed schemes. Numerical experiments include the Sod shock tube problem, vortex advection and flow past a NACA0012 airfoil.
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2012-31
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Seminar for Applied Mathematics, ETH Zurich
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03851 - Mishra, Siddhartha / Mishra, Siddhartha