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JOURNALS // Sibirskii Zhurnal Industrial'noi Matematiki // Archive

Sib. Zh. Ind. Mat., 2018 Volume 21, Number 4, Pages 15–27 (Mi sjim1018)

This article is cited in 9 papers

Numerical solution of a fluid filtration problem in a fractured medium by using the domain decomposition method

V. I. Vasil'eva, M. V. Vasil'evaa, V. S. Gladkikhb, V. P. Ilinbc, D. Ya. Nikiforova, D. V. Perevozkinb, G. A. Prokop'eva

a Ammosov North-Eastern Federal University, ul. Belinskogo 58, Yakutsk, 677000 Russia
b Institute of Computational Mathematics and Mathematical Geophysics, pr. Akad. Lavrent'eva 6, Novosibirsk, 630090 Russia
c Novosibirsk State University, ul. Pirogova 2, Novosibirsk, 630090 Russia

Abstract: Under consideration are the numerical methods for simulation of a fluid flow in fractured porous media. The fractures are taken into account explicitly by using a discrete fracture model. The formulated single-phase filtering problem is approximated by an implicit finite element method on unstructured grids that resolve fractures at the grid level. The systems of linear algebraic equations (SLAE) are solved by the iterative methods of domain decomposition in the Krylov subspaces using the KRYLOV library of parallel algorithms. The results of solving some model problem are presented. A study is conducted of the efficiency of the computational implementation for various values of contrast coefficients which significantly affect the condition number and the number of iterations required for convergence of the method.

Keywords: filtering, fracturedmedium, discrete fracture model, approximation, flow rate, finite element method, unstructured grid, iterative method.

UDC: 519.632.4

Received: 18.06.2018

DOI: 10.17377/sibjim.2018.21.402


 English version:
Journal of Applied and Industrial Mathematics, 2018, 12:4, 785–796

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© Steklov Math. Inst. of RAS, 2024