Simulation of hydro-deformation coupling problem in unsaturated porous media using exponential SWCC and hybrid improved iteration method with multigrid and multistep preconditioner

IF 5.6 1区 工程技术 Q1 ENGINEERING, GEOLOGICAL Acta Geotechnica Pub Date : 2024-09-20 DOI:10.1007/s11440-024-02414-9
Shuairun Zhu, Lulu Zhang, Lizhou Wu
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Abstract

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.

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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
基于渗流-变形耦合控制方程的数值模型常用于模拟非饱和多孔介质中的土壤流体力学和变形。其中,以压力水头为主要变量的 Picard 迭代法因其简便性和处理部分饱和条件的能力而被广泛使用。众所周知,该方法在一些不利的流动条件下容易收敛失败,而且计算耗时。本研究利用指数函数描述的非饱和土的土水特征曲线(SWCC)对耦合方程进行线性化处理,以克服非线性常微分方程的重复组装问题。采用六节点三角形有限元法对耦合控制方程进行离散线性化。此外,经典的高斯-赛德尔迭代法(GS)可用于求解由线性化耦合方程生成的线性方程。然而,GS 的收敛速度严重限制了线性方程的非线性条件,尤其是当线性方程的条件数远大于 1.0 时。因此,我们提出了一种结合多步预处理和级联多网格的改进型高斯-赛德尔迭代方法 MP(m)-GSCMGI。通过数值实例验证了所提方法在模拟非饱和多孔介质中可变饱和流动和变形中的适用性。结果表明,与传统的 Picard 和 GS 相比,所提出的改进方法具有更快的收敛速度和计算效率。混合改进方法 MP(m)-GSCMGI 可以实现更稳健的收敛和更经济的模拟。
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来源期刊
Acta Geotechnica
Acta Geotechnica ENGINEERING, GEOLOGICAL-
CiteScore
9.90
自引率
17.50%
发文量
297
审稿时长
4 months
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.
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