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Entropy analysis and entropy stable DG methods for the 1D...
[Submitted on 6 Feb 2026 (v1), last revised 23 Jun 2026 (this ve · 2026-06-24 · via math updates on arXiv.org

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Abstract:We demonstrate that the one-dimensional shallow water moment equations satisfy an auxiliary entropy conservation law, where the entropy function corresponds to the total energy. Additionally, we show that the classical Newtonian slip friction and Manning friction terms are entropy dissipative with respect to the developed entropy variables. The results from the continuous entropy analysis are used to construct an entropy stable and well-balanced nodal discontinuous Galerkin spectral element method for the spatial approximation. Key to ensure the entropy stability of the scheme is the derivation of entropy conservative numerical fluxes that satisfy a discrete version of the entropy flux compatibility condition. Finally, numerical examples demonstrate the performance of the scheme and validate the theoretical results.

Submission history

From: Patrick Ersing [view email]
[v1] Fri, 6 Feb 2026 09:10:16 UTC (393 KB)
[v2] Tue, 23 Jun 2026 08:42:01 UTC (400 KB)