  In this work, we focus on the numerical approximation of the shallow water
equations in two space dimensions. Our aim is to propose a well-balanced,
all-regime and positive scheme. By well-balanced, it is meant that the scheme
is able to preserve the so-called lake at rest smooth equilibrium solutions. By
all-regime, we mean that the scheme is able to deal with all flow regimes,
including the low-Froude regime which is known to be challenging when using
usual Godunov-type finite volume schemes. At last, the scheme should be
positive which means that the water height stays positive for all time. Our
approach is based on a Lagrange-projection decomposition which allows to
naturally decouple the acoustic and transport terms. Numerical experiments on
unstructured meshes illustrate the good behaviour of the scheme.

Numerical Analysis;Analysis of PDEs;Classical Physics