Implementing a discontinuous Galerkin method for the compressible, inviscid Euler equations in the DUNE framework | Zendy

GallegoValencia Juan Pablo | Zendy; Löbbert Johannes | Zendy; Müthing Steffen | Zendy; Bastian Peter | Zendy; Klingenberg Christian | Zendy; Xia Yinhua | Zendy

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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)

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