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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2016, Volume 56, Number 6, Pages 1082–1092
DOI: https://doi.org/10.7868/S0044466916060107
(Mi zvmmf10400)
 

This article is cited in 20 scientific papers (total in 20 papers)

Hybrid numerical method with adaptive overlapping meshes for solving nonstationary problems in continuum mechanics

N. G. Buragoa, I. S. Nikitinb, V. L. Yakushevb

a Institute for Problems of Mechanics, Russian Academy of Sciences, pr. Vernadskogo 101, korp. 1, Moscow, 119526, Russia
b Institute for Computer-Aided Design, Russian Academy of Sciences, ul. Vtoraya Brestskaya 19/18, Moscow, 123056, Russia
References:
Abstract: Techniques that improve the accuracy of numerical solutions and reduce their computational costs are discussed as applied to continuum mechanics problems with complex time-varying geometry. The approach combines shock-capturing computations with the following methods: (1) overlapping meshes for specifying complex geometry; (2) elastic arbitrarily moving adaptive meshes for minimizing the approximation errors near shock waves, boundary layers, contact discontinuities, and moving boundaries; (3) matrix-free implementation of efficient iterative and explicit-implicit finite element schemes; (4) balancing viscosity (version of the stabilized Petrov–Galerkin method); (5) exponential adjustment of physical viscosity coefficients; and (6) stepwise correction of solutions for providing their monotonicity and conservativeness.
Key words: matrix-free finite element method exponential adjustment of physical viscosity, overlapping adaptive meshes, fluid flow, large elastoplastic deformations.
Funding agency Grant number
Russian Foundation for Basic Research 15-08-02392_а
Received: 09.11.2015
English version:
Computational Mathematics and Mathematical Physics, 2016, Volume 56, Issue 6, Pages 1065–1074
DOI: https://doi.org/10.1134/S0965542516060105
Bibliographic databases:
Document Type: Article
UDC: 519.634
Language: Russian
Citation: N. G. Burago, I. S. Nikitin, V. L. Yakushev, “Hybrid numerical method with adaptive overlapping meshes for solving nonstationary problems in continuum mechanics”, Zh. Vychisl. Mat. Mat. Fiz., 56:6 (2016), 1082–1092; Comput. Math. Math. Phys., 56:6 (2016), 1065–1074
Citation in format AMSBIB
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  • This publication is cited in the following 20 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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