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arXiv · 2403.17123

A high-order explicit Runge-Kutta approximation technique for the Shallow Water Equations

Jean-Luc Guermond·Matthias Maier·Eric Tovar
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Abstract

We introduce a high-order space-time approximation of the Shallow Water Equations with sources that is invariant-domain preserving (IDP) and well-balanced with respect to rest states. The employed time-stepping technique is a novel explicit Runge-Kutta (ERK) approach which is an extension of the class of ERK-IDP methods introduced by Ern and Guermond (SIAM J. Sci. Comput. 44(5), A3366--A3392, 2022) for systems of non-linear conservation equations. The resulting method is then numerically illustrated through verification and validation.

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Jean-Luc Guermond, Matthias Maier, Eric Tovar. 2024-03-25. A high-order explicit Runge-Kutta approximation technique for the Shallow Water Equations. https://doi.org/10.1016/j.compfluid.2024.106493

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