Résumé : The numerical simulation of sediment transport problems is considered.The problem is modeled through the shallow-water equations coupled with the Exner equation to describe the time evolution of the bed prole. The Grass model is used for the sediment transport. The governing equations arediscretized by using two different finite-volume methods, the SRHN predictorcorrector scheme and a Modied Roe scheme for non conservative systems of equations. As for the time advancing, starting from the explicit versions, linearised implicit schemes are generated, in which the fl ux Jacobians are computed through automatic dierentiation. This allows the complexity of the analytical differentiation of the numerical schemes to be avoided. Second-order accuracy in space and time is obtained through MUSCL reconstruction together with a defect-correction approach. Finally the considered numerical ingredients are compared in terms of accuracy and computational time using different one dimensional and two dimensional sediment transport problems, characterised by different time scales for the evolution of the bed and of the water flow.