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.
@article{arxiv.2403.17123,
title = {A high-order explicit Runge-Kutta approximation technique for the Shallow Water Equations},
author = {Jean-Luc Guermond and Matthias Maier and Eric Tovar},
journal= {arXiv preprint arXiv:2403.17123},
year = {2025}
}