High Performance Computing Linear Algorithms for Two-Phase Flow in Porous Media

  • Robert Eymard
  • Cindy Guichard
  • Roland MassonEmail author
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 78)


We focus here on the difficult problem of linear solving, when considering implicit scheme for two-phase flow simulation in porous media. Indeed, this scheme leads to ill-conditioned linear systems, due to the different behaviors of the pressure unknown (which follows a diffusion equation) and the saturation unknown (mainly advected by the total volumic flow). This difficulty is enhanced by the parallel computing techniques, which reduce the choice of the possible preconditioners. We first present the framework of this study, and then we discuss different algorithms for linear solving. Finally, numerical results show the performances of these algorithms.


Injection Well Implicit Scheme Newton Iteration Wall Clock Time Saturation Variation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  1. 1.Laboratoire d’Analyse et de Mathématiques AppliquéesCNRS, UPEM, UPECChamps-sur-MarneFrance
  2. 2.Laboratoire Jacques-Louis Lions, CNRS, UMR 7598Sorbonne Universités, UPMC Univ Paris 06ParisFrance
  3. 3.Laboratoire de Mathématiques J.A. Dieudonné, UMR CNRS 7251 and team CoffeeUniversité Nice Sophia Antipolis, CNRS and INRIA Sophia Antipolis MéditerranéeNiceFrance

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