山区河流平面二维水沙数学模型研究

Research on Plane 2-D Flow and Sediment Mathematical Model and Its Application in Mountain River

根据泥沙交换原理,建立了河道非均匀沙悬移质水流挟沙力及推移质输沙率的计算模式,将非均匀沙推移质与床沙的交换形式概化为单向淤积、单向冲刷及淤粗冲细3种基本形式,并建立了每种交换形式下的非均匀沙推移质有效输沙率的计算公式.针对天然河道边界复杂及天然河道长宽尺寸一般相差悬殊的特点,本文采用正交贴体网格.在此基础上建立了正交曲线贴体坐标系下的平面二维全沙数学模型.采用有限体积法对拟合坐标系下的水沙基本控制方程进行了离散,在求解过程中采用了欠松弛技术和逐线迭代法.在北盘江坝油滩河道中对水位、水流流速以及河床冲淤等进行了验证计算及分析.数值实验表明,该模型能正确地模拟山区河流复杂的水流以及河床的冲刷、淤积过程.

On the basis of mechanism of sediment exchange, some improvements in relation to the calculation method for river-bed deformation are performed. The sediment transport model of non-homogeneous bed load is established. The exchange forms between the bed load and riverbed are divided into three types, sole depositions, sole erosion, and deposition of the coarser one and erosion of the finer ones. Different types result from different sources of sediment and result in different formulas of effective transport rate of bed load. A plane 2-D full load mathematical model is established under the body-fitted coordinate system based on staggered grid. In this model, the finite volume method is adopted to disperse the basic governing equations. The SIMPLEC （Semi-Implicit Method for Pressure-linked Equations Consistent ） algorithm, relaxation technique and line-by-line method are used in solution of the discrete equations, which can improve the convergence and stability of computation. The water level, velocity and riverbed deformation are verified by the field data in Bayoutan Reach of Beipanjiang River. The results show that the flow field and the process of riverbed erosion and deposition in mountain river can be simulated correctly by this method.