Comparison of new efficient 2D models for the simulation of bedload transport using the augmented Roe approach

Abstract

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≤O(10−3). If the interaction factor G is medium or high, G>O(10−2), 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.