Comparison of explicit and implicit time advancing in the simulation of a 2D Sediment transport problem

The simulation of sediment transport, based on the shallow-water equations coupled with Grass model for the sediment transport equation is considered. for the morphodynamic, namely the Exner equation and the . The aim of the present paper is to investigate the behavior of implicit linearized schemes in this context. The equations are discretized in space through a finite-volume approach A finite-volume method is considered and second-order accuracy in space is obtained through MUSCL reconstruction. A second-order time accurate explicit version of the scheme is obtained through a two step Runge-Kutta method. Implicit linearized schemes of second-order of accuracy in time are derived thanks to a Defect Correction technique. The different time-advancing schemes are compared, using a 2D sediment transport problem, with different types of flow/bed interactions. The implicit one largely outperforms the explicit version for slow flow/bed interactions while in the case of fast flow/bed interactions, the CPU time of both time integration schemes are comparable. Thus, the implicit scheme turns out to be a good candidate to simulate flows with sediment transport in practical applications.