基于Lattice Boltzmann方法的洪水演进模拟

Flood Routing Based on Diffusion Wave Equation Using Lattice Boltzmann Method

采用离散方法求解圣维南方程组的简化形式来推求下游断面未来洪水过程是目前洪水演算中最为常见的水力学方法。但这种方法存在的数值不稳定、计算速度慢等问题,也是目前宏观方法描述流体运动的一个挑战。Lattice Boltzmann方法以粒子速度分布函数为研究对象,在求解非线性偏微分方程组时,将非线性偏微分方程组转化为Lattice Boltzmann演进方程,从而变为简单的线性方程,使得计算效率得到大大提高。研究选用线性扩散波方程来描述河道洪水波运动,采用对空间坐标不进行多尺度处理,而对时间坐标引入五个时间尺度的多尺度展开方式,建立了线性扩散波方程的Lattice Boltzmann方法D1Q5速度模型,进而推求下断面洪水过程。文中分别采用Muskingum法、解析解法和Lattice Boltzmann方法的D1Q5速度模型对长江上游龙街—乔家河段、湖南资水柘溪水电站下游江南—夫溪河段进行洪水演算,3种方法的洪峰相对误差、峰现时间、确定性系数模拟的结果相似,从而验证了Lattice Boltzmann方法的准确性。同时分析了时间步长、空间步长和弛豫时间的选取对计算精度的影响。结果表明:Lattice Boltzmann方法可以很好的预测洪水过程,且计算效率较宏观方法得到大大提高,空间步长的取值比时间步长的取值对精度的影响大,在进行洪水演算时,应结合上下游断面长度,选取合适的空间步长,弛豫时间τ的取值不宜过大,建议在[1.5,3]范围内为宜。

Actually,for the flood routing,one of the most common hydraulic methods is the discrete method for the simplified form of the Saint-Venant equations.However,this method has some problems such as numerical instability and slow calculation speed.It is also a challenge for the description of fluid motion by the macroscopic method.The Lattice Boltzmann Method takes the distribution function as the research object.In solving nonlinear partial differential equations,there is a need for transforming it into the Lattice Boltzmann Evolution Equation which is a simple linear equation for solving the slow calculation speed of the macroscopic method.In this paper,the linear diffusion wave equation is used to describe the flood wave motion in the river channel.Instead of using the space coordinate,it adopts the multi-scale expansion method with five time scales to establish the D1Q5 model of Lattice Boltzmann Method for the linear diffusion wave equation and then to inquire into the inference of the flood process of downstream.The Muskingum Method,analytical solution method and the D1Q5 model of Lattice Boltzmann Method applied in flood computation at the Longjie-Qiaojia upper reaches of the Changjiang River and JiangnanFuxi downstream reaches of one hydropower station in Hunan Province.The simulation results of the flood peak relative error,peak appearance time and deterministic coefficient of the three methods are similar,which verifies the accuracy of Lattice Boltzmann Method.In addition,the influences of step length and relaxation time on calculation accuracy are also analyzed.The results show that the Lattice Boltzmann Method can effectively predict the flood process.And compared with the macroscopic method,the computational efficiency is greatly improved.The selection of space step value has a greater influence on calculation accuracy than the time step value.The appropriate space step should be selected,combined with the upstream and downstream section length.The value of the relaxation time is appropriate within the range of[1.5,3].