Stream Channel stability. Appendix K. Two-Dimensional Finite-Element Model for Routing Water and Sediment in Short Alluvial Channel Reaches

摘要

The objective of this study is to develop a new methodology for modeling the phenomenon of sediment movement in irregular alluvial channels, scouring around obstructions, etc. The basic physical principles of conservation of mass and momentum are used to describe the fluid flow. The conservation of mass and semi-empirical equations governing sediment particle movement are adopted to establish the interaction between the sediment movement and the fluid flow. The resulting mathematical model is, unfortunately, highly nonlinear and complex. It is impractical, if not impossible, to solve it analytically. Therefore, the numerical methods of finite element and finite difference are used to obtain approximate solutions of this model. The application of the finite element method (FEM) to model fluid flows has progressed rapidly in recent years from the simplest linear inviscid fluid flow problems (Martin, 1968; Argyris et al., 1969) to slow viscous flows (Tong, 1969; Atkinson et al., 1969; Oden and Sornogyi, 1969), and finally to the solution of full Navier-Stokes equations (Oden, 1970; Skiba, 1970; Olson, 1972; Oden and Wellford, 1972). However, this latter area represents an extremely large and complex field. As such, the research, although very active, can only be referred to as being in its beginning stage (Olson, 1975). A summary of its recent applications to flows through porous media, shallow water circulation, and two-dimensional viscous flows had been presented by Connor and Brebbia (1976).