Modeling Alluvial‐Channel Flow by Multimode Characteristics Method

Abstract

Unsteady flows in movable‐bed open channels can be described by a set of three partial differential equations: the equations of continuity and motion for sediment‐laden flow and the equation of continuity for sediment. It is possible to develop a genuinely coupled flow‐simulation model by solving the three equations simultaneously. The equations are first transformed into a set of characteristic equations that are organized for numerical solution by the method of characteristics (MOC). However, the characteristic values representing water‐wave and bed‐deformation propagation have great disparity in this class of unsteady‐flow models; this poses significant difficulty in model treatment. The multimode numerical scheme presented herein is believed to be particularly suitable for treating such disparity because of its ability to apply automatically a most appropriate computational mode to each type of characteristic. With this new scheme, mathematically effective and physically sensitive coupling can be attained. Theoretical considerations, mathematical derivations, and algorithm formulation that lead to, and guide, the development of a basic simulation model are presented in this paper.