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Multirate Undrained Splitting for Coupled Flow and Geomechanics in Porous Media

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Numerical Mathematics and Advanced Applications ENUMATH 2015

Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 112))

Abstract

We consider a multirate iterative scheme for the quasi-static Biot equations modelling the coupled flow and geomechanics in a porous medium. The iterative scheme is based on undrained splitting where the flow and mechanics equations are decoupled with the mechanics solve followed by the pressure solve. The multirate scheme proposed here uses different time steps for the two equations, that is, uses q flow steps for each coarse mechanics step and may be interpreted as using a regularization parameter for the mechanics equation. We prove the convergence of the scheme and the proof reveals the appropriate regularization parameter and also the effect of the number of flow steps within coarse mechanics step on the convergence rate.

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Acknowledgements

K. Kumar acknowledges the support of Statoil-UiB Akademia grant that allowed him to travel to ENUMATH conference at Ankara and CSM, ICES, UT Austin for the hospitality where part of the work was completed.

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Authors and Affiliations

  1. Mathematics Institute, University of Bergen, Bergen, Norway

    Kundan Kumar

  2. CSM, ICES, UT Austin, USA

    Tameem Almani, Gurpreet Singh & Mary F. Wheeler

Authors
  1. Kundan Kumar
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  2. Tameem Almani
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  3. Gurpreet Singh
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  4. Mary F. Wheeler
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Corresponding author

Correspondence to Kundan Kumar .

Editor information

Editors and Affiliations

  1. Mathematics & Applied Mathematics, Middle East Technical University Mathematics & Applied Mathematics, Ankara, Turkey

    Bülent Karasözen

  2. Dept of Computer Engg, Middle East Technical Univ Dept of Computer Engg, Cankaya, Ankara, Turkey

    Murat ManguoÄŸlu

  3. Middle East Technical University Mathematics & Institute of Applied Mathe, Ankara, Turkey

    Münevver Tezer-Sezgin

  4. Civil Engineering & Applied Mathematics, Middle East Technical University, Ankara, Turkey

    Serdar Göktepe

  5. Institute of Applied Mathematics, Middle East Technical University Institute of Applied Mathematics, Ankara, Turkey

    Ömür Uğur

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© 2016 Springer International Publishing Switzerland

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Kumar, K., Almani, T., Singh, G., Wheeler, M.F. (2016). Multirate Undrained Splitting for Coupled Flow and Geomechanics in Porous Media. In: Karasözen, B., Manguoğlu, M., Tezer-Sezgin, M., Göktepe, S., Uğur, Ö. (eds) Numerical Mathematics and Advanced Applications ENUMATH 2015. Lecture Notes in Computational Science and Engineering, vol 112. Springer, Cham. https://doi.org/10.1007/978-3-319-39929-4_41

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