Well-balanced bicharacteristic-based scheme for multilayer shallow water flows including wet/dry fronts

The aim of this paper is to present a new well-balanced finite volume scheme for two-dimensional multilayer shallow water flows including wet/dry fronts. The ideas, presented here for the two-layer model, can be generalized to a multilayer case in a straightforward way. The method developed here is constructed in the framework of the Finite Volume Evolution Galerkin (FVEG) schemes. The FVEG methods couple a finite volume formulation with evolution operators. The latter are constructed using the bicharacteristics of multidimensional hyperbolic systems. However, in the case of multilayer shallow water flows the required eigenstructure of the underlying equations is not readily available. Thus we approximate the evolution operators numerically. This approximation procedure can be used for arbitrary hyperbolic systems. We derive a well-balanced approximation of the evolution operators and prove that the FVEG scheme is well-balanced for the multilayer lake at rest states even in the presence of wet/dry fronts. Several numerical experiments confirm the reliability and efficiency of the new well-balanced FVEG scheme.