We propose a space–time discontinuous Galerkin (DG) method to approximate multi-dimensional non-conservative hyperbolic systems. The scheme is based on a particular choice of interface fluctuations. The key difference with existing space–time DG methods lies in the fact that our scheme is formulated in entropy variables, allowing us to prove entropy stability for the method. Additional numerical stabilization in the form of streamline diffusion and shock-capturing terms are added. The resulting method is entropy stable, arbitrary high-order accurate, fully discrete, and able to handle complex domain geometries discretized with unstructured grids. We illustrate the method with representative numerical examples.
Accepté le :
DOI : 10.1051/m2an/2017056
Mots-clés : Multidimensional nonconservative hyperbolic systems, space–time discontinuous Galerkin methods, entropy-stability, streamline diffusion, shock-capturing methods, two-layer shallow water system.
@article{M2AN_2018__52_3_995_0,
author = {Hiltebrand, Andreas and Mishra, Siddhartha and Par\'es, Carlos},
title = {Entropy-stable space{\textendash}time {DG} schemes for non-conservative hyperbolic systems},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
pages = {995--1022},
publisher = {EDP-Sciences},
volume = {52},
number = {3},
year = {2018},
doi = {10.1051/m2an/2017056},
mrnumber = {3865556},
zbl = {1405.65121},
language = {en},
url = {http://archive.numdam.org/articles/10.1051/m2an/2017056/}
}
TY - JOUR AU - Hiltebrand, Andreas AU - Mishra, Siddhartha AU - Parés, Carlos TI - Entropy-stable space–time DG schemes for non-conservative hyperbolic systems JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2018 SP - 995 EP - 1022 VL - 52 IS - 3 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/m2an/2017056/ DO - 10.1051/m2an/2017056 LA - en ID - M2AN_2018__52_3_995_0 ER -
%0 Journal Article %A Hiltebrand, Andreas %A Mishra, Siddhartha %A Parés, Carlos %T Entropy-stable space–time DG schemes for non-conservative hyperbolic systems %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2018 %P 995-1022 %V 52 %N 3 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/m2an/2017056/ %R 10.1051/m2an/2017056 %G en %F M2AN_2018__52_3_995_0
Hiltebrand, Andreas; Mishra, Siddhartha; Parés, Carlos. Entropy-stable space–time DG schemes for non-conservative hyperbolic systems. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 52 (2018) no. 3, pp. 995-1022. doi : 10.1051/m2an/2017056. http://archive.numdam.org/articles/10.1051/m2an/2017056/
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