A high-order explicit Runge-Kutta approximation technique for the Shallow Water Equations
<|reference_start|>A high-order explicit Runge-Kutta approximation technique for the Shallow Water Equations: 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.<|reference_end|>
@article{guermond2024a,
    title={A high-order explicit Runge-Kutta approximation technique for the
  Shallow Water Equations},
    author={Jean-Luc Guermond, Matthias Maier, Eric Tovar},
    journal={arXiv preprint arXiv:2403.17123},
    year={2024},
    archivePrefix={arXiv},
    eprint={2403.17123},
    primaryClass={math.NA cs.NA}
}