Comparison of Explicit and Implicit Time Advancing in the Simulation of a 2D Sediment Transport Problem

Abstract

The simulation of sediment transport, based on the shallow-water equations coupled with Grass model for the sediment transport equation is considered. The aim of the present paper is to investigate the behavior of implicit linearized schemes in this context. 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 BDF method associated with 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. © Springer-Verlag Berlin Heidelberg 2011.