High-order finite volume modelling of one-dimensional flows

In this paper, a numerical model is presented, aiming at the accurate solution of the one-dimensional Shallow-water Equations with bed slope source terms. The numerical model, which is fully third-order precise in time and space, is based on the Spectral Volume Method, and makes use of the HLL approximate Riemann solver to evaluate the fluxes at the interfaces between the cells. The source terms are treated, in the context of the HLL solver, in an upwinded fashion. A number of numerical experiments are reported, showing the promising capabilities of the model to solve real-world problems with complicate topographies.