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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2014, Volume 54, Number 8, Pages 1345–1355
DOI: https://doi.org/10.7868/S0044466914080158 (Mi zvmmf10080) 		 
This article is cited in 14 scientific papers (total in 14 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, Bol’shaya Tul’skaya ul. 52, Moscow, 115191, Russia
b Ammosov North-Eastern Federal University, ul. Belinskogo 58, Yakutsk, 677000, Russia
Full-text PDF (230 kB) Citations (14)
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DOI: https://doi.org/10.7868/S0044466914080158
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.
Received: 10.02.2014
English version:
Computational Mathematics and Mathematical Physics, 2014, Volume 54, Issue 8, Pages 1305–1315
DOI: https://doi.org/10.1134/S0965542514080132
Bibliographic databases:
Document Type: Article
UDC: 519.634
MSC: 74B20, 76S05, 65N30
Language: Russian
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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    • This publication is cited in the following 14 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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