{"title":"利用指数 SWCC 以及多网格和多步预处理的混合改进迭代法模拟非饱和多孔介质中的水力变形耦合问题","authors":"Shuairun Zhu, Lulu Zhang, Lizhou Wu","doi":"10.1007/s11440-024-02414-9","DOIUrl":null,"url":null,"abstract":"<div><p>Numerical models based on seepage-deformation coupling governing equations are often used to simulate soil hydrodynamics and deformation in unsaturated porous media. Among them, Picard iteration method with pressure head as the main variable is widely used because of its simplicity and ability to deal with partial saturation conditions. It is well known that the method is prone to convergence failure under some unfavorable flow conditions and is also computationally time-consuming. In this study, the soil–water characteristic curve (SWCC) of unsaturated soil described by the exponential function is used to linearize the coupling equations to overcome the repeated assembly of nonlinear ordinary differential equations. The finite element method with six-node triangular element is used to discretely linearize the coupling governing equations. Further, the classical Gauss–Seidel iterative method (GS) can be used to solve the linear equations generated from the linearized coupling equations. However, the convergence rate of GS seriously restricts the ill-condition of the linear equations, especially when the condition number of linear equations is much larger than 1.0. Thus, we propose an improved Gauss–Seidel iterative methods MP(<i>m</i>)-GSCMGI by combining multistep preconditioning and cascadic multigrid. The applicability of the proposed methods in simulating variably saturated flow and deformation in unsaturated porous media is verified by numerical examples. The results show that the proposed improved methods have faster convergence rate and computational efficiency than the conventional Picard and GS. The hybrid improved method MP(<i>m</i>)-GSCMGI can achieve more robust convergence and economical simulation.</p></div>","PeriodicalId":49308,"journal":{"name":"Acta Geotechnica","volume":null,"pages":null},"PeriodicalIF":5.6000,"publicationDate":"2024-09-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Simulation of hydro-deformation coupling problem in unsaturated porous media using exponential SWCC and hybrid improved iteration method with multigrid and multistep preconditioner\",\"authors\":\"Shuairun Zhu, Lulu Zhang, Lizhou Wu\",\"doi\":\"10.1007/s11440-024-02414-9\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>Numerical models based on seepage-deformation coupling governing equations are often used to simulate soil hydrodynamics and deformation in unsaturated porous media. Among them, Picard iteration method with pressure head as the main variable is widely used because of its simplicity and ability to deal with partial saturation conditions. It is well known that the method is prone to convergence failure under some unfavorable flow conditions and is also computationally time-consuming. In this study, the soil–water characteristic curve (SWCC) of unsaturated soil described by the exponential function is used to linearize the coupling equations to overcome the repeated assembly of nonlinear ordinary differential equations. The finite element method with six-node triangular element is used to discretely linearize the coupling governing equations. Further, the classical Gauss–Seidel iterative method (GS) can be used to solve the linear equations generated from the linearized coupling equations. However, the convergence rate of GS seriously restricts the ill-condition of the linear equations, especially when the condition number of linear equations is much larger than 1.0. Thus, we propose an improved Gauss–Seidel iterative methods MP(<i>m</i>)-GSCMGI by combining multistep preconditioning and cascadic multigrid. The applicability of the proposed methods in simulating variably saturated flow and deformation in unsaturated porous media is verified by numerical examples. The results show that the proposed improved methods have faster convergence rate and computational efficiency than the conventional Picard and GS. The hybrid improved method MP(<i>m</i>)-GSCMGI can achieve more robust convergence and economical simulation.</p></div>\",\"PeriodicalId\":49308,\"journal\":{\"name\":\"Acta Geotechnica\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":5.6000,\"publicationDate\":\"2024-09-20\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Acta Geotechnica\",\"FirstCategoryId\":\"5\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s11440-024-02414-9\",\"RegionNum\":1,\"RegionCategory\":\"工程技术\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"ENGINEERING, GEOLOGICAL\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Acta Geotechnica","FirstCategoryId":"5","ListUrlMain":"https://link.springer.com/article/10.1007/s11440-024-02414-9","RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"ENGINEERING, GEOLOGICAL","Score":null,"Total":0}
Simulation of hydro-deformation coupling problem in unsaturated porous media using exponential SWCC and hybrid improved iteration method with multigrid and multistep preconditioner
Numerical models based on seepage-deformation coupling governing equations are often used to simulate soil hydrodynamics and deformation in unsaturated porous media. Among them, Picard iteration method with pressure head as the main variable is widely used because of its simplicity and ability to deal with partial saturation conditions. It is well known that the method is prone to convergence failure under some unfavorable flow conditions and is also computationally time-consuming. In this study, the soil–water characteristic curve (SWCC) of unsaturated soil described by the exponential function is used to linearize the coupling equations to overcome the repeated assembly of nonlinear ordinary differential equations. The finite element method with six-node triangular element is used to discretely linearize the coupling governing equations. Further, the classical Gauss–Seidel iterative method (GS) can be used to solve the linear equations generated from the linearized coupling equations. However, the convergence rate of GS seriously restricts the ill-condition of the linear equations, especially when the condition number of linear equations is much larger than 1.0. Thus, we propose an improved Gauss–Seidel iterative methods MP(m)-GSCMGI by combining multistep preconditioning and cascadic multigrid. The applicability of the proposed methods in simulating variably saturated flow and deformation in unsaturated porous media is verified by numerical examples. The results show that the proposed improved methods have faster convergence rate and computational efficiency than the conventional Picard and GS. The hybrid improved method MP(m)-GSCMGI can achieve more robust convergence and economical simulation.
期刊介绍:
Acta Geotechnica is an international journal devoted to the publication and dissemination of basic and applied research in geoengineering – an interdisciplinary field dealing with geomaterials such as soils and rocks. Coverage emphasizes the interplay between geomechanical models and their engineering applications. The journal presents original research papers on fundamental concepts in geomechanics and their novel applications in geoengineering based on experimental, analytical and/or numerical approaches. The main purpose of the journal is to foster understanding of the fundamental mechanisms behind the phenomena and processes in geomaterials, from kilometer-scale problems as they occur in geoscience, and down to the nano-scale, with their potential impact on geoengineering. The journal strives to report and archive progress in the field in a timely manner, presenting research papers, review articles, short notes and letters to the editors.