The aim of this work is to develop an original semi-coupled approach for solving the Saint-Venant and Exner equation system. The shallow-water equations are solved first to calculate the full evolution of flow fields, and then the Exner equation is solved to model the morphodynamic response. The numerical method is based on a projection method, which consists in combining the momentum and continuity equations in order to establish a Poisson-type equation for water surface levels. The present formulation is identified as a semi-coupled approach because the projection method incorporates the change in the bed evolution in its approximation. A second-order numerical scheme has been proposed using an unstructured finite-volume technique and an implicit time integration method. Several benchmarks are used to demonstrate the capabilities, accuracy and performance of the model.

这项工作的目的是开发一种原始的半耦合方法来求解 Saint-Venant 和 Exner 方程组。首先求解浅水方程以计算流场的完整演化，然后求解 Exner 方程以模拟形态动力学响应。数值方法基于投影方法，包括组合动量和连续性方程，以建立水面水平的泊松型方程。本公式被确定为半耦合方法，因为投影方法在其近似值中包含了床演化的变化。已经提出了使用非结构化有限体积技术和隐式时间积分方法的二阶数值方案。几个基准测试用于演示功能，