• bedload
• grass
• meyer peter muller
• tunisi
• exner
• implicit scheme
• shallow water

The numerical simulation of sediment transport problems is considered. The physical problem is modeled through the shallow-water equations
coupled with the Exner equation to describe the time evolution of the bed profile. Three different models of solid transport discharge are considered. The spatial discretization of the governing equations is carried out by a finite-volume method and a modified Roe scheme designed for non-conservative systems. Linearized implicit schemes for time advancing are built through a recently proposed strategy, based on automatic differentiation to compute the flux Jacobians and on the defect correction approach to reach second-order accuracy. Explicit schemes for time advancing are compared with implicit ones in one-dimensional sediment transport problems, characterized by different time scales for the evolution of the bed. It is shown that, independently of the model used for the solid transport discharge, for slow and intermediate speeds of interaction between the bedload and the water flow, for which the use of large time steps is compatible with the capture of the bed evolution, implicit time advancing is far more efficient than explicit one with a CPU reduction up to more than four orders of magnitude. In the last part, a realistic test is proposed, concerning the sediment transport in Tunis Lake. This lake is divided into two main parts, the North Lake and South Lake. The simulations are performed setting input values to be consistent with reality, in order to have a good representation of sediment transport in Tunis Lake.