A semi-implicit Lagrange-projection-type finite volume scheme exactly well-balanced for 1D shallow-water system

Abstract

In this work we present a numerical approximation of the shallow water equations based on a Lagrangeprojection- type finite volume scheme. For the Lagrangian step we propose two different versions of the scheme, two explicit and other two semi-implicit that ensure first and second order of accuracy. The projection on the Eulerian coordinates will always be done explicitly, preserving the total order of the scheme. Special care is done for ensuring the well-balanced properties of the scheme. Several numerical experiments are included in order to illustrate the good behavior of the proposed schemes.