地下水溶质运移方程有限差分格式的实证研究  

Empirical Study of the Finite Difference Schemes of Solute Transport Equation in Groundwater

作　　者：焦甜[1] 王军霞[2] 唐仲华[1] 刘耿 

机构地区：[1]中国地质大学(武汉)环境学院,湖北武汉430074 [2]中国地质大学(武汉)数学与物理学院,湖北武汉430074 [3]北京得力合环境治理有限公司,北京100025

出　　处：《安全与环境工程》2016年第3期17-23,共7页Safety and Environmental Engineering

基　　金：中国博士后科学基金项目(201404406064);中国地质调查局项目(1212011121142)

摘　　要：在求解对流占优的地下水溶质运移方程时,为克服有限差分法和有限单元法产生的过量和值弥散等虚假数值现象,出现了许多数值方法,其中包括Crank-Nicholson格式、上游加权法和人工扩散量法等。以一维地下水溶质运移方程为例,分析三种差分格式的截断误差、稳定性和收敛性,并通过数值试验,在不同的对流强度下,将不同算法的数值解与解析解进行对比,研究不同算法的优缺点和适用条件。结果表明:在对流占优较弱时,三种方法都适用,但Crank-Nicholson差分格式误差最小;当对流强度增大时,适用时间步长较小的人工扩散量法;当对流强度较大时,适用时间步长较大的人工扩散量法,或者空间步长较小的上游加权法。该研究可为解决实际问题时算法的选择提供依据。In solving the advection-dominated solute transport equation in groundwater,in order to overcome the excess and numerical dispersion produced by finite-difference and finite element methods,many numerical methods are adopted,such as Crank-Nicholson scheme,upstream weighting method and artificial diffusion method.Taking the one-dimensional groundwater solute transport equation as an example,this paper analyses the truncation error,stability and convergence of the three difference schemes,and compares the numerical solutions of different algorithms with the analytical solutions in different advection-dominated intensities through numerical experiments in order to explore the advantages and disadvantages and applicable conditions of different algorithms.The results indicate that when the advection-dominated intensity is weak,all the methods are applicable,while the error of CN scheme is the minimum;with the increasing advection-dominated intensity,the artificial diffusion method with smaller time step is applicable;once the advection-dominated intensity is relatively strong,the artificial diffusion method with larger time step or the upstream weighting method with smaller space step is applicable.This research provides a basis for the selection of algorithm for solving the practical problems.

关 键 词：地下水溶质运移方程 对流占优强度 有限差分格式 解析解 实证对比 

分 类 号：X143[环境科学与工程—环境科学] P641.2[天文地球—地质矿产勘探]