Generalized Multiscale Finite Element method for multicontinua unsaturated flow problems in fractured porous media
Publication in refereed journal

香港中文大學研究人員
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摘要In this paper, we present a multiscale method for simulations of the multicontinua unsaturated flow problems in heterogeneous fractured porous media. The mathematical model is described by the system of Richards equations for each continuum that is coupled by the specific transfer term. To illustrate the idea of our approach, we consider a dual continua background model with discrete fractures networks that is generalized as a multicontinua model for unsaturated fluid flow in the complex heterogeneous porous media. We present fine grid approximation based on the finite element method and Discrete Fracture Model (DFM) approach. In this model, we construct an unstructured fine grid that takes into account complex fracture geometries for two and three dimensional formulations. Due to construction of the unstructured grid, the fine grid approximation leads to the very large system of equations. For reduction of the discrete system size, we develop a multiscale method for coarse grid approximation of the coupled problem using Generalized Multiscale Finite Element Method (GMsFEM). In this method, we construct coupled multiscale basis functions that are used to construct highly accurate coarse grid approximation. The multiscale method allowed us to capture detailed interactions between multiple continua. The adaptive approach is investigated, where we consider two approaches for multiscale basis functions construction: (1) based on the spectral characteristics of the local problems and (2) using simplified multiscale basis functions. We investigate accuracy of the proposed method for the several test problems in two and three dimensional formulations. We present a comparison of the relative error for different number of basis functions and for adaptive approach. Numerical results illustrate that the presented method provides accurate solution of the unsaturated multicontinua problem on the coarse grid with huge reduction of the discrete system size.
著者Denis Spiridonov, Maria Vasilyeva, Eric T. Chung
期刊名稱Journal of Computational and Applied Mathematics
出版年份2020
月份5
卷號370
出版社Elsevier
文章號碼112594
國際標準期刊號0377-0427
電子國際標準期刊號1879-1778
語言美式英語

上次更新時間 2020-14-09 於 00:15