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Numerical Solution of Thermoporoelasticity Problems

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Numerical Analysis and Its Applications (NAA 2016)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10187))

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Abstract

We consider the numerical solution of thermoporoelasticity problems. The basic system of equations includes the Lame equation for the displacement and two nonstationary equations for the fluid pressure and temperature. The computational algorithm is based on the finite element approximation in space and the finite difference approximation in time. We construct standard implicit scheme and unconditionally stable splitting schemes with respect to physical processes, when the transition to a new time level is associated with solving separate sub-problems for the desired displacement, pressure, and temperature. The stability of the scheme is achieved by passing to three-level difference scheme and by choosing a weight used as a regularization parameter. We provide the stability condition of the splitting scheme and present numerical experiments supporting this condition.

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Acknowledgements

This research was supported by RFBR (project N14-01-00785A).

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Authors and Affiliations

  1. North-Eastern Federal University, Yakutsk, Russia

    Alexandr E. Kolesov & Petr N. Vabishchevich

  2. University of North Carolina at Charlotte, Charlotte, North Carolina, 28223, USA

    Alexandr E. Kolesov

  3. Nuclear Safety Institute, RAS, Moscow, Russia

    Petr N. Vabishchevich

Authors
  1. Alexandr E. Kolesov
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  2. Petr N. Vabishchevich
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Correspondence to Alexandr E. Kolesov .

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Editors and Affiliations

  1. Institute of Information and Communication Technologies, Bulgarian Academy of Sciences, Sofia, Bulgaria

    Ivan Dimov

  2. Department of Applied Analysis, Eötvös Loránd University, Budapest, Hungary

    István Faragó

  3. Department of Applied Mathematics and Statistics, University of Rousse, Ruse, Bulgaria

    Lubin Vulkov

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Kolesov, A.E., Vabishchevich, P.N. (2017). Numerical Solution of Thermoporoelasticity Problems. In: Dimov, I., Faragó, I., Vulkov, L. (eds) Numerical Analysis and Its Applications. NAA 2016. Lecture Notes in Computer Science(), vol 10187. Springer, Cham. https://doi.org/10.1007/978-3-319-57099-0_47

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  • DOI: https://doi.org/10.1007/978-3-319-57099-0_47

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-57098-3

  • Online ISBN: 978-3-319-57099-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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