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Zh. Vychisl. Mat. Mat. Fiz., 2016, Volume 56, Number 6, Pages 1082–1092 (Mi zvmmf10400)  

This article is cited in 6 scientific papers (total in 6 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

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


DOI: https://doi.org/10.7868/S0044466916060107

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English version:
Computational Mathematics and Mathematical Physics, 2016, 56:6, 1065–1074

Bibliographic databases:

UDC: 519.634
Received: 09.11.2015

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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\yr 2016
\vol 56
\issue 6
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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. A. V. Favorskaya, “Interpolation on unstructured tetrahedral grids”, Innovations in Wave Processes Modelling and Decision Making: Grid-Characteristic Method and Applications, Smart Innovation Systems and Technologies, 90, eds. A. Favorskaya, I. Petrov, Springer-Verlag, Berlin, 2018, 45–73  crossref  mathscinet  isi  scopus
    2. N. G. Burago, I. S. Nikitin, “Algoritmy skvoznogo scheta dlya protsessov razrusheniya”, Kompyuternye issledovaniya i modelirovanie, 10:5 (2018), 645–666  mathnet  crossref
    3. N. G. Burago, A. B. Zhuravlev, I. S. Nikitin, “Kontinualnaya model i metod rascheta dinamiki neuprugoi sloistoi sredy”, Matem. modelirovanie, 30:11 (2018), 59–74  mathnet
    4. N. G. Burago, I. S. Nikitin, “Matrix-free conjugate gradient implementation of implicit schemes”, Comput. Math. Math. Phys., 58:8 (2018), 1247–1258  mathnet  crossref  crossref  isi  elib
    5. N. G. Bourago, A. D. Nikitin, I. S. Nikitin, B. A. Stratula, “Modelling of the microparticle spraying process in a heated gas stream”, Fundamental and Applied Problems of Mechanics-2017, IOP Conference Series-Materials Science and Engineering, 468, IOP Publishing Ltd, 2018, 012007  crossref  isi  scopus
    6. N. G. Burago, I. S. Nikitin, “Matematicheskaya model i algoritm rascheta pressovaniya i spekaniya”, Matem. modelirovanie, 31:2 (2019), 3–17  mathnet  crossref  elib
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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