Generalized Multiscale Finite Element Method for Unsaturated Filtration Problem in Heterogeneous Medium

机译：非均质介质中非饱和过滤问题的广义多尺度有限元方法

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We consider a mathematical model for simulation of the unsaturated flow problems in heterogeneous porous medium that describes by the Richards equation. To resolve all heterogeneity, we construct fine grid and construct finite element approximation. For dimension reduction of the discrete system, we construct multiscale solver for coarse grid solution using Generalized Multiscale Finite Element Method (GMsFEM). We generate multiscale basis functions by solution of the local spectral problems. We present numerical result and compare relative error for different number of the multiscale basis functions for 2D and 3D model problems.

机译：我们考虑由Richards方程描述的用于模拟非均质多孔介质中非饱和流动问题的数学模型。为了解决所有异质性，我们构造了精细网格并构造了有限元逼近。为了减少离散系统的尺寸，我们使用广义多尺度有限元方法（GMsFEM）构造了用于粗网格求解的多尺度求解器。我们通过解决局部频谱问题来生成多尺度基函数。我们给出了数值结果，并比较了2D和3D模型问题中不同数量的多尺度基函数的相对误差。

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《Finite difference methods: theory and applications》|2018年|517-524|共8页
会议地点 Lozenetz(BG)
作者
D. Spiridonov; M. Vasilyeva;
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作者单位

Multiscale Model Reduction Laboratory, North-Eastern Federal University, Yakutsk, Russia;

Multiscale Model Reduction Laboratory, North-Eastern Federal University, Yakutsk, Russia,Institute for Scientific Computation, Texas AM University, College Station, TX, USA;

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原文格式 PDF
正文语种 eng
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关键词
Heterogeneous media; Unsaturated filtration; Richards equation; Multiscale method; GMsFEM;

机译：异质媒体；不饱和过滤；理查兹方程；多尺度方法；有限元分析;

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1. An adaptive multiscale finite element method for unsaturated flow problems in heterogeneous porous media [J] . He Xinguang, Ren Li Journal of Hydrology . 2009,第1a2期

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2. Adaptive generalized multiscale finite element methods for H(curl)-elliptic problems with heterogeneous coefficients [J] . Chung Eric T., Li Yanbo Journal of Computational and Applied Mathematics . 2019,第期

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3. Generalized multiscale finite element methods for space-time heterogeneous parabolic equations [J] . Chung Eric T., Efendiev Yalchin, Leung Wing Tat, Computers & mathematics with applications . 2018,第2期

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4. Generalized Multiscale Finite Element Method for Unsaturated Filtration Problem in Heterogeneous Medium [C] . D. Spiridonov, M. Vasilyeva International Conference on Finite Difference Methods . 2019

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5. A STUDY OF FLUID INFILTRATION AND PROPAGATION OF VERTICAL HYDRAULIC FRACTURE IN A POROUS MEDIUM (DARCY'S LAW, FINITE-ELEMENT METHOD, DISPLACEMENT DISCONTINUITY, FLUID LEAK-OFF). [D] . CHIOU, YAW-JENQ. 1986

机译：多孔介质中垂直液压裂缝的渗流与扩散研究（达西定律，有限元方法，位移不连续性，渗漏）。
6. A Posteriori Error Estimates for Fully Discrete Finite Element Method for Generalized Diffusion Equation with Delay [O] . Wansheng Wang, Lijun Yi, Aiguo Xiao -1

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7. An Online Generalized Multiscale Finite Element Method for Unsaturated Filtration Problem in Fractured Media [O] . Denis Spiridonov, Maria Vasilyeva, Aleksei Tyrylgin, 2021

机译：裂缝介质中不饱和过滤问题的在线广义多尺度有限元方法

Generalized Multiscale Finite Element Method for Unsaturated Filtration Problem in Heterogeneous Medium

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