一维河网非恒定流及悬沙数学模型的节点控制方法

本文的一维河网非恒定流及悬沙数学模型，是根据以一维圣维南方程组，悬沙非平衡输运方程及水位、含沙量节点控制法而建立。首先，利用单一河流有限差分方程组转换形式和节点处质量、能量守恒性，写出所有节点的水位控制方程组。求解此不规则稀疏矩阵方程组得到得有节点的水位，再由单一河流非恒定流的求解方法可获得所有单一河流的断面水位和流量。基于水注的节点水位控制法，本文提出了节点悬沙控制法。假设节点处冲刷或淤积较小，所有节点的含沙量控制方程组可通过输沙量守恒方程用矩阵形式写出。求解此不规则稀疏矩阵方程组，得到所有节点处的含沙量。所有单一河流断面处的含沙量通过单一河流悬沙输运的求解方法获得。本文介绍的模型适用于各种河网类型。作为检验，该模型成功地应用于珠江三角洲流域河网水流及悬沙的数值计算。

Numerical model of unsteady flow and suspended-sediment transport in river networks with junction control method

A numerical model for simulating unsteady flow and suspended sediment transport in river networks was presented. This model was based on the Saint Venant equations and the non equilibrium transport equation for the suspended sediment, and the junction control methods for water level and sediment concentration were proposed. First, by utilizing the transforms of the single river finite difference equations and the mass and energy conservation at the river junction, the governing equations for the water level at all junctions cound be written in matrix form were obtained. The water level at all junctions were obtained by solving the irregular spare matrix equations, then the water level at all single river nodes were obtained with the algorithm for the single river unsteady flow. The algorithm for the sediment transport in river networks was similar to that for unsteady flow. This paper presents a junction control method for suspended sediment in river networks. It was assumed that the erosion and deposition at the junction is small, and the governing equations for the sediment concentration at all junctions can also be written in matrix form by the sediment mass conservation equation. Solving the irregular spare matrix equations, yielded the sediment concentration at all junctions. The sediment concentration at all single river nodes were resulted from the algorithm for the single river suspended sediment transport. The model presented in this paper is applicable to all river network types. As a check, the model was successfully used in the Pearl River networks.