Geodesic
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

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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.

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DOI : 10.1051/m2an/2017056
Classification : 65M60, 65M12, 35L60, 76L05
Keywords: Multidimensional nonconservative hyperbolic systems, space–time discontinuous Galerkin methods, entropy-stability, streamline diffusion, shock-capturing methods, two-layer shallow water system.

Hiltebrand, Andreas 1 ; Mishra, Siddhartha 1 ; Parés, Carlos 1

1 
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     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},
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     year = {2018},
     doi = {10.1051/m2an/2017056},
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     zbl = {1405.65121},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/m2an/2017056/}
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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

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