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Zh. Vychisl. Mat. Mat. Fiz., 2014, Volume 54, Number 8, Pages 1345–1355 (Mi zvmmf10080)  

This article is cited in 5 scientific papers (total in 5 papers)

Splitting scheme for poroelasticity and thermoelasticity problems

P. N. Vabishchevicha, M. V. Vasil'evab, A. E. Kolesovb

a Nuclear Safety Institute, Russian Academy of Sciences, BolТshaya TulТskaya ul. 52, Moscow, 115191, Russia
b Ammosov North-Eastern Federal University, ul. Belinskogo 58, Yakutsk, 677000, Russia

Abstract: Boundary value problems in thermoelasticity and poroelasticity (filtration consolidation) are solved numerically. The underlying system of equations consists of the Lamé stationary equations for displacements and nonstationary equations for temperature or pressure in the porous medium. The numerical algorithm is based on a finite-element approximation in space. Standard stability conditions are formulated for two-level schemes with weights. Such schemes are numerically implemented by solving a system of coupled equations for displacements and temperature (pressure). Splitting schemes with respect to physical processes are constructed, in which the transition to a new time level is associated with solving separate elliptic problems for the desired displacements and temperature (pressure). Unconditionally stable additive schemes are constructed by choosing a weight of a three-level scheme.

Key words: poroelasticity problem, thermoelasticity problem, finite element method, operator-difference schemes, splitting scheme.

DOI: https://doi.org/10.7868/S0044466914080158

Full text: PDF file (230 kB)
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English version:
Computational Mathematics and Mathematical Physics, 2014, 54:8, 1305–1315

Bibliographic databases:

UDC: 519.634
MSC: 74B20, 76S05, 65N30
Received: 10.02.2014

Citation: P. N. Vabishchevich, M. V. Vasil'eva, A. E. Kolesov, “Splitting scheme for poroelasticity and thermoelasticity problems”, Zh. Vychisl. Mat. Mat. Fiz., 54:8 (2014), 1345–1355; Comput. Math. Math. Phys., 54:8 (2014), 1305–1315

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. O. P. Iliev, A. E. Kolesov, P. N. Vabishchevich, “Numerical solution of plate poroelasticity problems”, Transp. Porous Media, 115:3, SI (2016), 563–580  crossref  mathscinet  isi  scopus
    2. A. E. Kolesov, P. N. Vabishchevich, “Numerical solution of thermoporoelasticity problems”, Numerical Analysis and Its Applications, NAA 2016, Lecture Notes in Computer Science, 10187, eds. I. Dimov, I. Farago, L. Vulkov, Springer, 2017, 422–429  crossref  mathscinet  zmath  isi  scopus
    3. A. E. Kolesov, P. N. Vabishchevich, “Splitting schemes with respect to physical processes for double-porosity poroelasticity problems”, Russ. J. Numer. Anal. Math. Model, 32:2 (2017), 99–113  crossref  mathscinet  zmath  isi  scopus
    4. V. N. Alekseev, M. V. Vasileva, G. A. Prokopev, A. A. Tyrylgin, “Modeli termouprugosti dlya poristykh materialov s uchetom nalichiya treschin”, Matematicheskie zametki SVFU, 24:3 (2017), 19–37  mathnet  crossref  elib
    5. M. V. Vasileva, P. E. Zakharov, P. V. Sivtsev, D. A. Spiridonov, “Chislennoe modelirovanie zadach termouprugosti dlya konstruktsii s vnutrennim istochnikom”, Matematicheskie zametki SVFU, 24:3 (2017), 52–64  mathnet  crossref  elib
  • ∆урнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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