An iterative modified multiscale control volume method for the simulation of highly heterogeneous porous media flow

  • L. M. C. Barbosa
  • A. R. E. Antunes
  • P. R. M. Lyra
  • D. K. E. Carvalho
Technical Paper


In this paper, a modification of the multiscale finite-volume method (MsFVM) in its OBMM version (operator-based multiscale method) is introduced. The iterative modified multiscale control volume method (I-MMCVM) is applied to solve the elliptical problem that describes the single-phase fluid flow through heterogeneous porous media. The modifications proposed are accomplished by: (1) resettling the vertices, centroid of the primal coarse volume, of each primal coarse volume laying on the boundary of the computational domain, and by this, avoiding the use of ghost elements; (2) Recalculating the pressure iteratively in each primal coarse volume to improve the accuracy of the solution lost during the process of decoupling the problem in sub-problems. The I-MMCVM achieves efficiently accurate results for flow equations in highly heterogeneous reservoirs, at very low computational cost whilst it recovers physical consistency whenever the multiscale solution fails and produces nonphysical results. The I-MMCVM solution is compared with the fine mesh solution for some highly heterogeneous media. In terms of efficiency, the novel method showed great potential of the multiscale formulations, i.e., computational cost reduction without significant loss of accuracy.


Iterative multiscale finite volume method Single-phase flow Highly heterogeneous porous media Reservoir simulation 



The authors gratefully acknowledge the financial support provide by the Brazilian Research Councils CNPq, FINEP, The Pernambuco Research Agency FACEPE, PRH26-ANP, and CENPESPETROBRAS.


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Copyright information

© The Brazilian Society of Mechanical Sciences and Engineering 2018

Authors and Affiliations

  • L. M. C. Barbosa
    • 1
  • A. R. E. Antunes
    • 2
  • P. R. M. Lyra
    • 1
  • D. K. E. Carvalho
    • 1
  1. 1.Mechanical Engineering DepartmentFederal University of PernambucoRecifeBrazil
  2. 2.Technology CenterFederal University of PernambucoCaruaruBrazil

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