饱和–非饱和渗流的数值流形法研究与应用  

Saturated-unsaturated seepage by numerical manifold method

作　　者：陈远强 杨永涛[1] 郑宏[1,3] 李伟[1,2] 林姗 CHEN Yuan-qiang;YANG Yong-tao;ZHENG Hong;LI Wei;LIN Shan(State Key Laboratory of Geomechanics and Geotechnical Engineering,Institute of Rock and Soil Mechanics,Chinese Academy of Sciences,Wuhan 430071,China;University of Chinese Academy of Sciences,Beijing 100049,China;College of Architecture and Civil Engineering,Beijing University of Technology,Beijing 100124,China)

机构地区：[1]中国科学院武汉岩土力学研究所岩土力学与工程国家重点实验室,湖北武汉430071 [2]中国科学院大学,北京100049 [3]北京工业大学建筑工程学院,北京100124

出　　处：《岩土工程学报》2019年第2期338-347,共10页Chinese Journal of Geotechnical Engineering

基　　金：国家自然科学基金项目(11172313;11572009;51538001;51609240);国家重点基础研发计划("973"计划)项目(2014CB047100)

摘　　要：非饱和渗流问题涉及岩土、水利和环境等众多领域,合理有效地模拟非饱和渗流过程具有重要意义。基于数值流形方法(numerical manifold method,NMM)的覆盖思想,建立了非饱和渗流Richards方程的NMM离散格式,相比于有限元方法(finite element method,FEM),NMM的前处理更为灵活,对复杂边界具有更强的适应性。欠松弛技术和集中质量矩阵的引入,有效抑制了求解过程中的数值震荡现象。通过对一维和二维非饱和渗流算例的模拟,验证了算法的有效性与可靠性。The unsaturated seepage problem involves many fields,such as geotechnical engineering,hydraulic engineering and environmental engineering.So it is of great significance to simulate the unsaturated flow reasonably and effectively.Based on the cover system of numerical manifold method(NMM),a NMM discrete form is established to solve the Richards equation for the unsaturated flow.Compared with finite element method(FEM),NMM is more flexible in the preprocessing,and more adaptable to complex boundary conditions.By introducing the under-relaxation technique and the lumped mass matrix,the numerical oscillation is eliminated.Through the simulations of 1D and 2D unsaturated seepage problems,the validity and reliability of the proposed algorithm are verified.

关 键 词：非饱和渗流 RICHARDS方程 数值流形方法 集中质量矩阵 数值震荡 

分 类 号：TV139.14[水利工程—水力学及河流动力学]