Numerical modelling of two-dimensional morphodynamics with applications to river bars and bifurcations

摘要

We study the numerical approximation of the two-dimensional morphodynamic model governed by the shallow water and Exner equations to simulate reach-scale two-dimensional morphodynamics of bedload-dominated alluvial rivers. The solution strategy relies on a full coupling of the governing equations within each time step. The resulting system of governing equations contains nonconservative products related to the longitudinal and lateral bed slopes and source terms related to friction. The full problem is solved numerically on unstructured triangular grids, simultaneously updating the principal part and adding the source terms (friction) using a splitting technique.The principal part is solved by means of a novel second-order accurate upwind-biased centred scheme of the finite volume type, while the source terms are added to the problem by solving a system of ordinary differential equations. A new algorithm for treating the wetting-and-drying is also proposed. The model is applied to well-established test problems in order to verify the accuracy of the proposed method, the robustness of the wetting-and-drying algorithm and the ability of the model in dealing with transcritical flows. Finally we test the model ability to reproduce two dimensional morphodynamic processes occurring at the scale of tens of channel widths in bedload dominated alluvial rivers with homogeneous grain size. This is achieved by comparing model outcomes with those of analytical theories and flume experiments on the same morphodynamic processes. These selected "benchmarks" include migrating free bars spontaneously developing in straight reaches, steady bars forced by abrupt river planform changes and the dynamics of channel bifurcations.