采用改进的SOR迭代法模拟一维非饱和土渗流的研究  

Simulation of one-dimensional infiltration using improved SOR iterative methods in unsaturated soils

作　　者：罗晓辉 朱帅润 陈骄锐 吴礼舟[1,2] LUO Xiaohui;ZHU Shuairun;CHEN Jiaorui;WU Lizhou(State Key Laboratory of Geohazard Prevention and Geoenvironment Protection,School of Environment and Civil Engineering,Chengdu University of Technology,Chengdu 610059,China;State Key Laboratory of Mountain Bridge and Tunnel Engineering,Chongqing Jiaotong University,Chongqing 400074,China)

机构地区：[1]成都理工大学环境与土木工程学院,地质灾害防治与地质环境保护国家重点实验室,四川成都610059 [2]重庆交通大学省部共建山区桥梁及隧道工程国家重点实验室,重庆400074

出　　处：《中南大学学报（自然科学版）》2021年第9期3331-3340,共10页Journal of Central South University:Science and Technology

基　　金：国家自然科学基金资助项目(41790432)。

摘　　要：对一维RICHARDS方程进行线性化后,采用有限差分法(FDM)进行离散并获得一组线性方程,进而采用相应的迭代法进行求解。采用改进的预处理超松弛迭代法(P-SOR)和红黑排序超松弛迭代法(RB-SOR)求解线性方程组,同时,将改进的方法获得的数值解与解析解进行比较。研究结果表明:与传统的迭代法如GS、超松弛迭代法(SOR)相比,2种改进方法均可提高收敛率,且P-SOR比RB-SOR表现出更高的收敛率与计算效率。改进的SOR具有较好的数值精度和稳定性,并有显著的加速效果。该方法可以为地下水渗流的数值模拟提供参考。By linearizing the one-dimensional RICHARDS equation,the finite difference method(FDM)was used to discretize and a set of linear equations was obtained,then the RICHARDS equation was solved by the related iterative methods.The preconditioned successive over relaxation iteration method(P-SOR)and the red and black ordering successive over relaxation iteration method(RB-SOR)were used to solve linear equations.Meanwhile,the numerical solutions obtained by the improved methods were compared with the analytical solutions.The results show that compared with traditional iterative methods such as GS and SOR,the two improved iterative methods can improve the convergence rate,and P-SOR shows a faster convergence rate and a better computational efficiency than that of RB-SOR.The improved SOR has the high accuracy,strong stability and significant acceleration effect.This method can provide a reference for numerical simulation of groundwater flow.

关 键 词：非饱和土 RICHARDS方程 SOR迭代 红黑排序 预处理子 加速 

分 类 号：TU443[建筑科学—岩土工程]