Computational Geosciences

, Volume 17, Issue 3, pp 455–461 | Cite as

Convergence of iterative coupling for coupled flow and geomechanics

  • Andro Mikelić
  • Mary F. Wheeler
Original Paper


In this paper, we study solving iteratively the coupling of flow and mechanics. We demonstrate the stability and convergence of two widely used schemes: the undrained split method and the fixed stress split method. To our knowledge, this is the first time that such results have been rigorously obtained and published in the scientific literature. In addition, we propose a new stress split method, with faster convergence rate than known schemes. These results are specially important today due to the interest in hydraulic fracturing (Dean and Schmidt SPE J. 14:707–714, 2009; Ji et al. SPE J. 14:423–430, 2009; Samier and De Gennaro 2007; Settari and Maurits SPE J. 3:219–226, 1998), in oil and gas shale reservoirs.


Iterative splitting Geomechanics Biot system Darcy flow equation 

Mathematics Subject Classifications (2000)

35Q35 76M25 76S05 86Axx 


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Copyright information

© Springer Science+Business Media Dordrecht 2012

Authors and Affiliations

  1. 1.Université de Lyon, CNRS UMR 5208Université Lyon 1, Institut Camille JordanVilleurbanne CedexFrance
  2. 2.Center for Subsurface Modeling, Institute for Computational Engineering and SciencesThe University of TexasAustinUSA

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