A robust model for rapidly varying flows over movable bottom with suspended and bedload transport: Modelling and numerical approach

•We deduced a new model for suspended and bedload sediment transport.•The model was deduced without using the Boussinesq hypothesis.•The hyperbolic system is solved using a fast and robust PVM path conservative scheme.•An efficient way to implement the erosion-deposition source term is applied.•The global numerical scheme is positivity preserving. We propose a coupled model for suspended and bedload sediment transport in the shallow water framework. The model is deduced under hydrostatic pressure assumptions and will not assume any Boussinesq hypothesis. The numerical resolution is carried out in a segregated way. First the underlying system of conservation laws is solved by using a first order path-conservative Riemann solver. Then, the source terms corresponding with the erosion and depositions rates are approximated in a semi-implicit way. The final scheme preserves the positivity of the density. Several numerical experiments were carried out in order to validate the model and the numerical scheme. The results obtained are in good agreement with the experimental data.