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

  • D. SpiridonovEmail author
  • M. Vasilyeva
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11386)


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.


Heterogeneous media Unsaturated filtration Richards equation Multiscale method GMsFEM 



Work is supported by the mega-grant of the Russian Federation Government (N 14.Y26.31.0013 and RFBR N 17-01-00732).


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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Multiscale Model Reduction Laboratory, North-Eastern Federal UniversityYakutskRussia
  2. 2.Institute for Scientific ComputationTexas A&M UniversityCollege StationUSA

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