Algebraic multiscale solver for flow in heterogeneous porous media

  • Authors:

  • Yixuan Wang;Hadi Hajibeygi;Hamdi A. Tchelepi

  • Affiliations:

  • Department of Energy Resources Engineering, Stanford University, 367 Panama St., Rm. 065, Stanford, CA 94305-2220, USA;Department of Geoscience and Engineering, Faculty of Civil Engineering and Geosciences, Delft University of Technology, P.O. Box 5048, 2600 GA Delft, The Netherlands and Department of Energy Resou ...;Department of Energy Resources Engineering, Stanford University, 367 Panama St., Rm. 065, Stanford, CA 94305-2220, USA

  • Venue:
  • Journal of Computational Physics
  • Year:
  • 2014

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Abstract

An Algebraic Multiscale Solver (AMS) for the pressure equations arising from incompressible flow in heterogeneous porous media is described. In addition to the fine-scale system of equations, AMS requires information about the superimposed multiscale (dual and primal) coarse grids. AMS employs a global solver only at the coarse scale and allows for several types of local preconditioners at the fine scale. The convergence properties of AMS are studied for various combinations of global and local stages. These include MultiScale Finite-Element (MSFE) and MultiScale Finite-Volume (MSFV) methods as the global stage, and Correction Functions (CF), Block Incomplete Lower-Upper factorization (BILU), and ILU as local stages. The performance of the different preconditioning options is analyzed for a wide range of challenging test cases. The best overall performance is obtained by combining MSFE and ILU as the global and local preconditioners, respectively, followed by MSFV to ensure local mass conservation. Comparison between AMS and a widely used Algebraic MultiGrid (AMG) solver [1] indicates that AMS is quite efficient. A very important advantage of AMS is that a conservative fine-scale velocity can be constructed after any MSFV stage.