The aim of this work is to construct efficient finite volume schemes for the numerical study of sediment transport in shallow water, in the framework of the Exner model.In most cases, the velocity related to the sediment is much lower that the fluid velocity, which, in turn, may be much lower that the free-surface wave speed. Explicit methods that resolve all waves require small time steps due to the CFL stability restriction because of fast surface waves. Furthermore, if Rusanov flux is adopted, slow sediment waves may be affected by the large numerical diffusion. The objective of the present work is to drastically improve the efficiency in the computation of the evolution of the sediment by treating water waves implicitly, thus allowing much larger time steps than the one required by fully explicit schemes. The goal is reached by suitably semi-implicit schemes obtained by the use of implicit-explicit Runge-Kutta methods.

翻译：本文旨在构建高效的有限体积格式，用于Exner模型框架下浅水沉积物输运的数值研究。在大多数情况下，与沉积物相关的速度远低于流体速度，而流体速度又可能远低于自由表面波速。由于快表面波的CFL稳定性限制，解析所有波的显式方法需要较小的步长。此外，若采用Rusanov通量，慢沉积波可能受到较大数值扩散的影响。本研究的目标是通过隐式处理水波，从而允许比完全显式格式所需步长大得多的时间步长，显著提高沉积物演化的计算效率。通过使用隐式-显式Runge-Kutta方法构造合适的半隐式格式，实现了上述目标。