A well-balanced spectral volume scheme with the wetting-drying property for the shallow-water equations

In this paper a numerical model for the solution of the one-dimensional shallow-water equations with bed slope source terms is presented. The numerical model, that is third-order accurate in wet regions, far from discontinuities of the flow field, is based on the Spectyral Volume Method, and makes use of the HLLE approximate Riemann solver to evaluate the fluxes at the interfaces between the spectral cells. In order to ensure the C-Property, the source terms are upwinded at the interfaces, after a so-called "hydrostatic reconstruction": the sub-gridding property of the Spectral Volume Method is exploited, in order to ensure the well-balancing of the algorithm also at the wet-dry frontiers. A number of numerical experiments are reported, that show the promising capabilities of the model to solve real-world problems with complicate topographies.