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

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.

arXiv comment29 pages, 9 figures

References in corpus (6)

• SWASHES: a compilation of Shallow Water Analytic Solutions for Hydraulic and Environmental Studies
• Invariant domain preserving discretization-independent schemes and convex limiting for hyperbolic systems
• Third and fourth order well-balanced schemes for the shallow water equations based on the CWENO reconstruction
• Multi-GPU implementation of a time-explicit finite volume solver for the Shallow-Water Equations using CUDA and a CUDA-Aware version of OpenMPI
• Bound-preserving and entropy-stable algebraic flux correction schemes for the shallow water equations with topography
• On a numerical artifact of solving shallow water equations with a discontinuous bottom: Analysis and a nontransonic fix