On discretely entropy conservative and entropy stable discontinuous Galerkin methods

Author
Chan, Jesse
Year 2017
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Abstract

High order methods based on diagonal-norm summation by parts operators can be shown to satisfy a discrete conservation or dissipation of entropy for nonlinear systems of hyperbolic PDEs. These methods can also be interpreted as nodal discontinuous Galerkin methods with diagonal mass matrices. In this work, we describe how to construct discretely entropy conservative schemes to a more general class of DG methods using flux differencing, quadrature-based projections, and specific DG differentiation operators. This approach also recovers existing methods for Burgers' equation involving dense norm and generalized SBP operators without boundary nodes. Numerical experiments confirm the stability and high order accuracy of the proposed methods for the one-dimensional compressible Euler equations.

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Details

Title
On discretely entropy conservative and entropy stable discontinuous Galerkin methods
Author
Chan, Jesse
Year
2017
Type
Research Article
Language
eng
History*
2017-08-03 00:00:00 · 2017-08-06 00:00:00
Categories
Numerical Analysis

Fields edited by Q-Sensei or Q-Sensei's users are marked with an asterisk (*).
This is Version 2 of this record. Q-Sensei Corp. added this version on August 9, 2017. It is an edited version of the original data import from arXiv.org e-Print archive. View changes to the previous version or view the complete version history.