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In this work, we focus on the numerical approximation of the shallow waterequations 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 schemeis able to preserve the so-called lake at rest smooth equilibrium solutions. Byall-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 usingusual Godunov-type finite volume schemes. At last, the scheme should bepositive which means that the water height stays positive for all time. Ourapproach is based on a Lagrange-projection decomposition which allows tonaturally decouple the acoustic and transport terms. Numerical experiments onunstructured meshes illustrate the good behaviour of the scheme.

An all-regime and well-balanced Lagrange-projection type scheme for the shallow water equations on unstructured meshes