The bedload transport system of equations, composed by the two-dimensional shallow water equations for the free surface flow motion and the 2D Exner or bedload transport equation for the erodible bed layer, is used for a wide range of sediment transport processes in environmental surface flows. In this work, the numerical resolution has been implemented using improved and efficient versions of two different strategies for combining the hydrodynamical and morphodynamical components of the system. The first strategy is based on the full coupling of the flow and bedload transport equations (FCM), leading to a new formulation for the intercell numerical fluxes which includes the bed elevation into the resolution of the approximated local Riemann problem (RP) at the edges. The stability region of this method is controlled by the eigenvalues of the coupled Jacobian matrix at each intercell edge. On the second hand, an alternative decoupled strategy is considered based on solving independently the shallow water and the bed transport equations at each time step but controlling the stability region by means of an approximation of the coupled Jacobian matrix eigenvalues. This method, called approximate-coupled (ACM) allows simpler expressions for the numerical fluxes at the edges and ensures the stability of the scheme. Both strategies are based on the Finite Volume (FV) method using Roe’s approach for the computation of the numerical fluxes between neighbouring cells and have been implemented into the same CPU-based numerical kernel in order to perform a realistic comparison of the range of applicability and computational efficiency. The ACM can only guarantee non-oscillatory results when the bed-flow interaction factor is small $G\le \mathcal{O}\left({10}^{-3}\right)$. If the interaction factor $G$ is medium or high, $G>\mathcal{O}\left({10}^{-2}\right)$, the decoupled scheme loses its accuracy and robustness. Furthermore, for highly erosive flows the FCM scheme demonstrates to be more efficient in terms of computational effort than the ACM, one of the key points for large-scale and long-term bedload transport realistic applications.

由二维浅水方程的自由表面流运动和二维Exner或可侵蚀床层的床载方程组成的方程式基床输运系统，可用于环境表层流中的各种泥沙输运过程。 。在这项工作中，使用两种不同策略的改进和有效版本来实现数值分辨率，以结合系统的水动力和形态动力组件。第一种策略是基于流动和床载输运方程（FCM）的完全耦合，从而得出一种新的单元间数值通量公式，其中包括将床高升高到边缘处的近似局部Riemann问题（RP）的分辨率中。该方法的稳定性区域由每个小区间边缘处耦合的雅可比矩阵的特征值控制。另一方面，考虑了另一种解耦策略，该策略基于在每个时间步长独立解决浅水和床层运移方程，但通过耦合雅可比矩阵特征值的近似值来控制稳定区域。这种称为近似耦合（ACM）的方法可以简化边沿数值通量的表达式，并确保方案的稳定性。两种策略都基于有限体积（FV）方法，该方法使用Roe方法计算相邻单元之间的数值通量，并且已在同一基于CPU的数值内核中实现，以便对适用范围和适用范围进行现实的比较。计算效率。仅当床流相互作用因子较小时，ACM才能保证无振荡结果$G\le \mathcal{Ø}（{10}^{-3}）$。如果相互作用因素$G$ 中或高 $G>\mathcal{Ø}（{10}^{-\mathrm{2个}}）$，解耦方案失去了准确性和鲁棒性。此外，对于高度侵蚀性的流，FCM方案在计算工作量方面比ACM更为有效，而ACM是大规模和长期床载运输现实应用的关键点之一。