准二维非恒定非均匀泥沙数学模型

在一雏非恒定非均匀泥沙数学模型研究的基础上，提出了可以模拟横向冲淤变形以及河宽变化的准二维非恒定非均匀泥沙数学模型．将横断面沿河道流向分成若干个流管，对每个流管利用非耦合法分别求解水流方程和泥沙方程．运用Preissmann四点偏心隐式格式对水流连续方程和运动方程进行离散，并用追赶法求解．采用迎风格式将悬移质连续方程离散成差分方程求解．根据最小能耗率原理，判别河床冲淤变化方向，以确定河宽是否变化、该模型弥补了以往大多数准二维泥沙数学模型只能按等流量划分流管，且只能模拟恒定流、均匀沙、固定河宽情况下的河床冲淤变化的缺陷．利用青铜峡水库实测的水沙资料，对所建立的模型进行了验证，计算结果与实测值吻合良好．

Quasi-2D Mathematical Model for Nonuniform Sediment Transport in Unsteady Flow

On the basis of 1-D mathematical model for nonuniform sediment transport in unsteady flow, a quasi-2D mathematical model for nonuniform sediment transport in unsteady flowwas set up to simulate transverse lateral deformation of erosion or deposition and change of river width. Following the flow direction of channel, transverse section of the channel was divided into several stream tubes. Then the 1-D mathematical model was used in every tube. The flow equations were differenced by Preissmann scheme, and the difference equations were solved with pursuit method. The continuity equation of suspended load was solved by up-wind difference scheme. The theory of minimum rate of energy dissipation was introduced to the model to judge change of river width. Previous quasi-2D models can only divide the tubes according to uniform discharge and simulate the deformation of erosion or deposition of uniform sediment transport in steady flow in the river with fixed width. This model makes up these limitations. The model was verified by the measured water and sand data of Qingtongxia reservoir, and calculated results were in good agreement with measured values.