New spacetime discontinuous Galerkin methods for solving convection-diffusion systems
Abstract
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 [17]. 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
Publication status
publishedExternal links
Journal / series
SAM Research ReportVolume
Publisher
Seminar for Applied Mathematics, ETH ZurichSubject
Discontinuous Galerkin method; Entropy stability; Convection-diffusion systems; Compressible Navier-Stokes equationOrganisational unit
03851 - Mishra, Siddhartha / Mishra, Siddhartha
Funding
306279 - Structure preserving approximations for robust computation of conservation laws and related equations (EC)
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