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.

翻译：我们提出了一种针对带源项浅水方程的高阶时空近似方法，该方法具有不变域保持性（IDP）且在静止状态下保持良态平衡。所采用的时间推进技术是一种新型显式龙格-库塔（ERK）方法，该方法是对Ern与Guermond（SIAM J. Sci. Comput. 44(5), A3366--A3392, 2022）针对非线性守恒方程组提出的ERK-IDP方法类别的扩展。最终通过验证与确认对所得方法进行了数值演示。