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Implementing a discontinuous Galerkin method for the compressible, inviscid Euler equations in the DUNE framework
Author(s) -
GallegoValencia Juan Pablo,
Löbbert Johannes,
Müthing Steffen,
Bastian Peter,
Klingenberg Christian,
Xia Yinhua
Publication year - 2014
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201410457
Subject(s) - inviscid flow , riemann solver , discontinuous galerkin method , classification of discontinuities , euler equations , mathematics , riemann problem , compressibility , mathematical analysis , bounded function , riemann hypothesis , physics , mechanics , finite volume method , finite element method , thermodynamics
A discontinuous Galerkin scheme was implemented in the DUNE framework to solve the compressible, inviscid Euler equations in a multi‐dimensional Cartesian grid. It uses a HLLC Riemann solver for the numerical fluxes in the interfaces, a total variation bounded limiter to handle discontinuities, a positivity preserving limiter for near vacuum conditions, and adaptive mesh refinement (AMR). (© 2014 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)