Finite volume approximation of the Linearized shallow water equations in hyperbolic mode

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 ũ0, ṽ0 and φ0 (sub- or super-critical flow at each part of the boundary). The three cases that we consider are fully hyperbolic modes.