Finite Volume Approximation of the Linearized Shallow Water Equations in Hyperbolic Mode

Abstract

In this article, we consider the linearized inviscid shallow water equations in space dimension two in a rectangular domain. We implement a finite volume discretization and prove the numerical stability and convergence of the scheme for three cases that depend on the background flow $\tilde{u}_0$, $\tilde{v}_0$, and $\tilde{\phi}_0$ (sub- or super-critical flow at each part of the boundary). The three cases that we consider are fully hyperbolic modes.