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Russian Journal of Numerical Analysis and Mathematical Modelling

Editor-in-Chief: Dymnikov, Valentin P. / Kuznetsov, Yuri

Managing Editor: Vassilevski, Yuri V.

Editorial Board: Agoshkov, Valeri I. / Amosov, Andrey A. / Kaporin, Igor E. / Kobelkov, Georgy M. / Mikhailov, Gennady A. / Repin, Sergey I. / Shaidurov, Vladimir V. / Shokin, Yuri I. / Tyrtyshnikov, Eugene E.

IMPACT FACTOR 2017: 0.662

CiteScore 2017: 0.71

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Volume 32, Issue 2


Splitting schemes with respect to physical processes for double-porosity poroelasticity problems

Alexander E. Kolesov / Petr N. Vabishchevich
  • Corresponding author
  • Nuclear Safety Institute of the RAS, B. Tulskaya 52, Moscow 113191, Russia
  • RUDN University, Moscow 117198, Russia
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Published Online: 2017-04-24 | DOI: https://doi.org/10.1515/rnam-2017-0009


We consider unsteady poroelasticity problem in fractured porous medium within the classical Barenblatt double-porosity model. For numerical solution of double-porosity poroelasticity problems we construct splitting schemes with respect to physical processes, where transition to a new time level is associated with solving separate problem for the displacements and fluid pressures in pores and fractures. The stability of schemes is achieved by switching to three-level explicit-implicit difference scheme with some of the terms in the system of equations taken from the lower time level and by choosing a weight parameter used as a regularization parameter. The computational algorithm is based on the finite element approximation in space. The investigation of stability of splitting schemes is based on the general stability (well-posedness) theory of operator-difference schemes. A priori estimates for proposed splitting schemes and the standard two-level scheme are provided. The accuracy and stability of considered schemes are demonstrated by numerical experiments.

Keywords: Poroelasticity; double-porosity; operator-difference schemes; splitting scheme; regularization

MSC 2010: 34Q74; 65M12; 65M60


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About the article

Received: 2016-11-14

Accepted: 2017-01-24

Published Online: 2017-04-24

Published in Print: 2017-04-01

Funding Source: Russian Foundation for Basic Research

Award identifier / Grant number: 14-01-00785

This work was supported by the Russian Foundation for Basic Research (project 14-01-00785) and by the Ministry of Education of the Russian Federation (Agreement No. 02.a03.21.0008 of June 24, 2016)

Citation Information: Russian Journal of Numerical Analysis and Mathematical Modelling, Volume 32, Issue 2, Pages 99–113, ISSN (Online) 1569-3988, ISSN (Print) 0927-6467, DOI: https://doi.org/10.1515/rnam-2017-0009.

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