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Accelerating the solution of linear systems appearing in two-phase reservoir simulation by the use of POD-based deflation methods |
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| Authors: | Diaz Cortés Gabriela Berenice Vuik Cornelis Jansen Jan-Dirk |
| Institution: | 1.Mexican Petroleum Institute (IMP), Eje Central Lazaro Cardenas Norte 152, Col. San Bartolo Atepehuacan, 07730, Mexico City, Mexico ;2.Delft University of Technology, Faculty of Electrical Engineering, Mathematics and Computer Science, Van Mourik Broekmanweg 6, 2628, XE, Delft, Netherlands ;3.Delft University of Technology, Faculty of Civil Engineering and Geosciences, Stevinweg 1, 2628, CN, Delft, Netherlands ; |
| 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. |
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