Coupled and splitting bedload sediment transport models based on a modified flux-wave approach

Numerical modeling of free-surface flow over a mobile bed with predominantly bedload sediment transport can be done by solving the shallow water and Exner equations using coupled and splitting approaches. The coupled method uses a coupling of the governing equations at the same time step leading to a non-conservative solution. The splitting method solves the Exner and the shallow water equations in a separate manner, and is only capable of modeling weak free-surface and bedload interactions. In the current study, an extended version of a Godunov-type wave propagation algorithm is presented for modeling of morphodynamic systems using both coupled and splitting approaches. In the introduced coupled method the entire morphodynamic system is solved in the form of a conservation law. For the splitting technique, a new wave Riemann decomposition is defined which enables the scheme to be utilized for mild and strong interactions. To consider the bedload sediment discharge within the Exner equation, the Smart and Meyer-Peter & Müller formulae are used. It was found that the coupled solution gives accurate predictions for all investigated flow regimes including propagation over a dry-state using a Courant-Friedrichs-Lewy (CFL) number equal to 0.6. Furthermore, the splitting method was able to model all flow regimes with a lower CFL number of 0.3.