A large time-step and well-balanced Lagrange-Projection type scheme for\n the shallow-water equations

Abstract

This work focuses on the numerical approximation of the Shallow Water\nEquations (SWE) using a Lagrange-Projection type approach. We propose to extend\nto this context recent implicit-explicit schemes developed in the framework of\ncompressibleflows, with or without stiff source terms. These methods enable the\nuse of time steps that are no longer constrained by the sound velocity thanks\nto an implicit treatment of the acoustic waves, and maintain accuracy in the\nsubsonic regime thanks to an explicit treatment of the material waves. In the\npresent setting, a particular attention will be also given to the\ndiscretization of the non-conservative terms in SWE and more specifically to\nthe well-known well-balanced property. We prove that the proposed numerical\nstrategy enjoys important non linear stability properties and we illustrate its\nbehaviour past several relevant test cases.\n