改进的Picard法在非饱和土渗流中的应用研究  

Application of improved Picard method in unsaturated seepage

作　　者：朱帅润 李绍红 何博 吴礼舟 ZHU Shuai-run;LI Shao-hong;HE Bo;WU Li-zhou(State Key Laboratory of Mountain Bridge and Tunnel Engineering,Chongqing Jiaotong University,Chongqing 400074,China;College of Environment and Civil Engineering,Chengdu University of Technology,Chengdu 610059,China;Department of Geological Engineering,Southwest Jiaotong University,Chengdu 610031,China)

机构地区：[1]重庆交通大学山区桥梁及隧道工程国家重点实验室,重庆400074 [2]成都理工大学环境与土木工程学院,四川成都610059 [3]西南交通大学地质工程系,四川成都610031

出　　处：《岩土工程学报》2022年第4期712-720,I0006,共10页Chinese Journal of Geotechnical Engineering

基　　金：国家重点研发计划项目(2018YFC1504702);国家自然科学基金项目(41790432);地质灾害防治与地质环境保护国家重点实验室自主课题(SKLGP2019Z010)。

摘　　要：Richards方程广泛应用于非饱和渗流的数值模拟以及其他相关领域。在数值求解中,可以采用有限体积法进行数值离散,进而采用Picard方法进行迭代求解。然而,为了获得可靠准确的数值解,通常均匀网格的空间步长是很小的,特别是在一些不利的数值条件下,比如降雨入渗于干燥土壤中,这往往使得迭代过程耗时,甚至不收敛。因此,结合Chebyshev形式的非均匀网格,提出了一种基于非均匀网格的两层网格校正法的改进Picard迭代方法(NTG-PI)。通过3个非饱和渗流算例,并与传统方法和解析解对比,对改进方法的数值精度、收敛率和加速效果进行了验证。结果表明,相对于传统的Picard方法和自适应松弛Picard方法,提出的方法NTG-PI可以在较少的离散节点数下获得较高的数值精度,以及较高的计算效率。该方法可以对非饱和渗流的数值模拟提供一定参考。Richards’equation is widely used in the simulation of unsaturated seepage and related fields.In the numerical solution,the finite volume method can be used for numerical discretization,and then the Picard method can be used for iterative solution.However,in order to obtain reliable and accurate numerical solutions,the spatial step size of a uniform grid is usually very small,especially under some unfavorable numerical conditions,such as rainfall infiltration into dry soil,which often makes the iterative process time-consuming or even unable to converge.Therefore,combined with the non-uniform grid in the form of Chebyshev,an improved Picard iteration method(NTG-PI)is proposed based on the non-uniform two-grid correction scheme.Through three examples of unsaturated seepage,the numerical accuracy,convergence rate and acceleration effect of the improved algorithm are validated by comparing the traditional methods and analytical solutions.The results show that compared with the traditional Picard and the adaptive relaxation Picard methods,the proposed method NTG-PI can obtain higher numerical accuracy with a smaller number of discrete nodes,and also has higher computational efficiency.The proposed method can provide a reference for the numerical simulation of unsaturated seepage.

关 键 词：非饱和渗流 Picard迭代 数值精度 非均匀网格 两层网格校正方法 

分 类 号：TU411.4[建筑科学—岩土工程]