Accelerating the solution of linear systems appearing in two-phase reservoir simulation by the use of POD-based deflation methods

Gabriela Berenice Diaz Cortes, Cornelis Vuik, Jan Dirk Jansen

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Abstract

We explore and develop a Proper Orthogonal Decomposition (POD)-based deflation method for the solution of ill-conditioned linear systems, appearing in simulations of two-phase flow through highly heterogeneous porous media. We accelerate the convergence of a Preconditioned Conjugate Gradient (PCG) method achieving speed-ups of factors up to five. The up-front extra computational cost of the proposed method depends on the number of deflation vectors. The POD-based deflation method is tested for a particular problem and linear solver; nevertheless, it can be applied to various transient problems, and combined with multiple solvers, e.g., Krylov subspace and multigrid methods.

Original languageEnglish
Pages (from-to)1621-1645
Number of pages25
JournalComputational Geosciences
Volume25
Issue number5
DOIs
Publication statusPublished - 2021

Keywords

  • Deflation
  • Krylov Methods
  • Porous media
  • Two-phase reservoir simulation

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