Numerical Solution of a Fluid Filtration Problem in a Fractured Medium by Using the Domain Decomposition Method

V. I. Vasil’ev, M. V. Vasil’eva, V. S. Gladkikh, V. P. Ilin, D. Ya Nikiforov, D. V. Perevozkin, G. A. Prokop’ev

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)

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 KRYLOVlibrary 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.

Original languageEnglish
Pages (from-to)785-796
Number of pages12
JournalJournal of Applied and Industrial Mathematics
Volume12
Issue number4
DOIs
Publication statusPublished - 1 Oct 2018

Keywords

  • approximation
  • discrete fracture model
  • filtering
  • finite element method
  • flow rate
  • fracturedmedium
  • iterative method
  • unstructured grid

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