A splitting scheme for the coupled Saint-Venant-Exner model

We present a splitting method for the one-dimensional Saint-Venant-Exner equations used describing bed evolution in shallow water systems. adapt flux vector approach of Toro and Vazquez-Cend\`on identify one subsystem conservative (advection system) non-conservative (pressure system), both having very simple eigenstructure compared to full system. The final numerical scheme is constructed using Godunov-type path-conservative pressure system Godunov advection solved following coupled solution strategy. resulting first-order accurate extended second order accuracy space time via ADER together with an AENO reconstruction technique. Accuracy, robustness well-balanced properties are assessed through carefully selected suite testcases. exceedingly simple, robust as sophisticated methods. A distinctive feature novel its flexibility choice sediment transport closure formula, which makes it particularly attractive scientific engineering applications.