Finite volume modelling of one-dimensional flows on movable bed

Modelling the flow propagation in shallow-water bodies with movable bed is a challenging task. Due to the existence of sediment transport, bottom discontinuities and sudden bed elevation changes can be developed, for example at the end of stilling basin aprons; moreover, it is common to find structures as drop structures, check dams, sills, which promote the formation of local bed discontinuities. Here, following the theory by Dal Maso, LeFloch and Murat, a numerical scheme is presented, which is well balanced and able to capture contact discontinuities in flows characterized by movable bed: in particular, the bed geometry non-conservative products are defined in order to ensure a hydrostatic pressure distribution onto the bed step. Finally, numerical tests are presented in order to demonstrate the viability of the method