坡面流格子Boltzmann方法与Preissmann隐式差分法模拟  

Comparison of Lattice Boltzmann Method and Preissmann Implicit Difference Method in Application to Overland Flow

作　　者：张小娜[1] 冯杰[2] 张东辉[3] 刘宁宁 

机构地区：[1]南京信息工程大学水文气象学院,南京210044 [2]中国水利水电科学研究院水资源研究所,北京100044 [3]江苏科技大学船舶与海洋工程学院,镇江212003 [4]山东省水利工程管理局,济南250013

出　　处：《农业机械学报》2014年第10期132-139,共8页Transactions of the Chinese Society for Agricultural Machinery

基　　金：国家自然科学基金资助项目(41301037);江苏省高校自然科学基础研究资助项目(11KJB170008);水利部公益性行业专项资助项目(201301040)

摘　　要：以D1Q5速度模型为例,时间多尺度分析为手段通过待定系数法来确定平衡态分布函数,将格子Boltzmann方法应用于坡面流运动方程;通过理想算例,以解析解为标准,比较了格子Boltzmann方法与应用广泛的Preissmann4点隐式差分法的计算精度。研究表明,对于模拟坡脚断面水深和单宽流量过程,格子Boltzmann方法的D1Q5模型的计算精度高于Preissmann 4点隐式差分法,尤其在退水阶段。对于达到平衡时间之前的坡面水深和坡面单宽流量,格子Boltzmann方法的D1Q5模型的计算精度也高于Preissmann 4点隐式差分法。但对于达到平衡时间之后的坡面水深和坡面单宽流量,格子Boltzmann方法的D1Q5模型在x=1 m点上出现了较大的相对误差,计算精度逊于Preissmann 4点隐式差分法。将格子Boltzmann方法应用于坡面流运动时,弛豫时间选择范围以[1,1.2]s为宜。Lattice Boltzmann method is applied extensively in the field of fluid motion for concise programming,parallel computing,and dealing with complex geometrical boundary easily and so on.As the main force of soil water erosion process,accurate simulation of the process of overland flow has important significance for analyzing the mechanism of slope erosion and building the physical process of soil erosion model.However,there is less research on the application of the lattice Boltzmann method to overland flow at present.In this paper,lattice Boltzmann method with D1Q5 velocity model is applied in motion equation of overland flow,in which,only time is considered in the process of multiple scales,and undetermined coefficient method is adopted to determine the equilibrium distribution function by means of multi-scale analysis.And then using analytical solution as a standard,lattice Boltzmann method and Preissmann four-point implicit scheme method are compared through ideal numerical example.The results indicate that the calculation precision of lattice Boltzmann method using D1Q5 velocity model is higher than that of Preissmann four-point implicit scheme method in simulating the variations of water depth and discharge per unit width at the bottom of slope,especially in the stage of recession flow,and in describing the distribution of water depth and discharge per unit width along the slope length before equilibrium time.But after equilibrium time,the calculation precision of lattice Boltzmann method using D1Q5 velocity model is lower in calculating the distribution of water depth and discharge per unit width along the slope length because at the point of x = 1 m,a large relative error occurs.The relaxation time is recommended to be taken in [1,1.2]s when lattice Boltzmann method is applied to solve the motion equation of overland flow.

关 键 词：坡面流 格子BOLTZMANN方法 Preissmann隐式差分法 D1Q5速度模型 弛豫时间 

分 类 号：P642.11[天文地球—工程地质学] TV122[天文地球—地质矿产勘探]