New spacetime discontinuous Galerkin methods for solving convection-diffusion systems
May, Sandra M.
In this paper, we present two new methods for solving systems of hyperbolic conservation laws with correct physical viscosity and heat conduction terms. In particular we are interested in solving the compressible Navier-Stokes equations. Both methods are extensions of the spacetime discontinuous Galerkin method for hyperbolic conservation laws developed by Hiltebrand and Mishra . Following this work, we use entropy variables as degrees of freedom and entropy stable finite volume fluxes. For the discretization of the diffusion term, we consider two different approaches: the interior penalty approach and a variant of the local discontinuous Galerkin method. For both approaches we show an entropy stability estimate. We also present numerical results in one dimension comparing both methods Show more
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Journal / seriesResearch Report
PublisherSeminar für Angewandte Mathematik, ETH Zürich
Organisational unit03851 - Mishra, Siddhartha
NotesAlso to be published in: Proceedings of XV International Conference on Hyperbolic Problems: Theory, Numerics, Applications.
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