Numerical Modeling of Aggradation and Degradation in Alluvial Channels

Abstract

The Saint‐Venant equations describing unsteady flow in open channels and the continuity equation for the conservation of sediment mass are numerically solved to determine the aggradation and degradation of channel bottom due to an imbalance between water flow and sediment discharge. For this purpose, the MacCormack explicit finite‐difference scheme is introduced. This scheme is second‐order accurate, handles shocks and discontinuities in the solution without any special treatment, and allows simultaneous solution of the water and sediment equations, thereby obviating the need for iterations. The sediment transport relationship in any form may be included in the computations. Computational procedures are outlined for incorporating the typical boundaries for hydraulic engineering applications. The mathematical model presented here is applied to predict (1) Bed‐level changes due to sediment overloading; (2) development of longitudinal profile due to base‐level lowering; (3) and bed‐level changes associated with the migration of knickpoints. The computed results are compared with the available experimental data obtained on laboratory flumes. The agreement between the computed and experimental results is satisfactory.