Bed evolution numerical model for rapidly varying flow in natural streams

A numerical model suitable for the reproduction of bed evolution in natural alluvial rivers and in channels of complex geometry is presented. It is based on a conservative formulation of one-dimensional shallow water equations, which includes an original treatment of the momentum equation source term. The proposed model has already been cross referenced with several test cases and experimental data found in the literature for fixed beds. In this study, however, the focus is on mobile bottom beds. The selected test cases are representative of some of the characteristic bed configurations that often occur in natural streams, and, therefore, are suitable for verifying the versatility of the model and its potential usefulness in the treatment of alluvial rivers. The MacCormack explicit finite difference scheme has been adopted for the numerical implementation. The liquid and solid phases are then solved by means of a semi-coupled procedure. A variety of bed evolution mechanisms and different water regime conditions are investigated in order to verify the model response in the cases of erosion, deposition and bed morphology evolution. The results show a good correspondence with the experimental data. Furthermore, the proposed model shows a notable numerical stability even when applied to test cases that are particularly difficult under the numerical computational profile, where the relative model of the standard formulation of the conservative balance equations shows evident numerical instability.