Application of Explicit Finite-Difference Schemes in Two-Dimensional Modeling of Flows in Deformable Channels

Abstract

Predicting the morphological evolution of river channels composed of easily erodible, fine-grained sediments is a recurring engineering problem, since many irrigation systems draw water through channels that are themselves prone to erosion and siltation. This paper presents a two-dimensional numerical model for simulating the morphological behavior of a river channel with a deformable bed. Sediment transport is described by a system of two-dimensional partial differential equations for the water–sediment mixture, expressing mass and momentum conservation in the form of the Saint-Venant equations, coupled with an explicit, grid-based scheme for bed and bank deformation that uses a minimal number of empirical coefficients. The model was tested against two independent sets of flume experiments - slope-leveling experiments at the Central Research Institute of Transport Construction (CRITC), and channel-quarry backfilling experiments at the State Hydrological Institute (SHI) - and its predictions were compared with the experimental data and with an independent numerical solution from the Research Institute of Power Engineering (RIPE). The proposed model reproduced the measured bed profiles with an accuracy comparable to, and in one case better than, the RIPE solution, with standard deviations from experimental data of 0.0019–0.0061 m across the tested time steps. The results demonstrate the significant contribution of bedload transport and the importance of interactions among water flow, sediment transport, and channel banks, while also indicating that, as with other models relying on empirical coefficients, further verification against field data is required.