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

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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. Burago^a, I. S. Nikitin^b, V. L. Yakushev^b

^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

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

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

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Linking options:

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This publication is cited in the following 20 articles:

A.D. Khanazaryan, M.V. Golub, “Hybrid method for modelling anti-plane vibrations of layered waveguides with bonded composite joints”, Comp. Contin. Mech., 16:1 (2023), 101
I. S. Nikitin, A. D. Nikitin, “Multirezhimnaya model i chislennyi algoritm rascheta kvazitreschin razlichnogo tipa pri tsiklicheskom nagruzhenii”, Kompyuternye issledovaniya i modelirovanie, 14:4 (2022), 873–885
I. S. Nikitin, N. G. Burago, A. D. Nikitin, “Damage and Fatigue Fracture of Structural Elements in Various Cyclic Loading Modes”, Mech. Solids, 57:7 (2022), 1793
M. V. Muratov, V. V. Ryazanov, V. A. Biryukov, D. I. Petrov, I. B. Petrov, “Inverse problems of heterogeneous geological layers exploration seismology solution by methods of machine learning”, Lobachevskii J. Math., 42:7, SI (2021), 1728–1737
N G Burago, A I Fedyushkin, “Numerical solution of the Stefan problem”, J. Phys.: Conf. Ser., 1809:1 (2021), 012002
A. I. Fedyushkin, N. G. Burago, A. A. Puntus, “Convective heat and mass transfer modeling under crystal growth by vertical Bridgman method”, Applied Mathematics, Computational Science and Mechanics: Current Problems, Journal of Physics Conference Series, 1479, IOP Publishing Ltd, 2020, 012029
Vasily I. Golubev, Maxim V. Muratov, Igor B. Petrov, Smart Innovation, Systems and Technologies, 173, Advances in Theory and Practice of Computational Mechanics, 2020, 199
Andrew A. Zhuravlev, Karine K. Abgaryan, Dmitry L. Reviznikov, Smart Innovation, Systems and Technologies, 173, Advances in Theory and Practice of Computational Mechanics, 2020, 225
Ilia S. Nikitin, Nikolay G. Burago, Vasily I. Golubev, Alexander D. Nikitin, Smart Innovation, Systems and Technologies, 173, Advances in Theory and Practice of Computational Mechanics, 2020, 171
N. G. Burago, I. S. Nikitin, “Mathematical model and algorithm for calculating pressing and sintering”, Math. Models Comput. Simul., 11:5 (2019), 731–739
N. G. Burago, I. S. Nikitin, A. D. Nikitin, B. A. Stratula, “Algorithms for calculation damage processes”, Frat. Integrita Strut., 2019, no. 49, 212–224
I. S. Nikitin, N. G. Burago, A. D. Nikitin, “Explicit-implicit schemes for solving the problems of the dynamics of isotropic and anisotropic elastoviscoplastic media”, 12Th International Conference - Mesh Methods For Boundary: Value Problems and Applications, Journal of Physics Conference Series, 1158, IOP Publishing Ltd, 2019, 032039
A. I. Fedyushkin, N. G. Burago, A. A. Puntus, “Effect of rotation on impurity distribution in crystal growth by bridgman method”, 4Th All-Russian Scientific Conference Thermophysics and Physical Hydrodynamics With the School For Young Scientists, Journal of Physics Conference Series, 1359, IOP Publishing Ltd, 2019, 012045
I S Nikitin, N G Burago, A D Nikitin, B A Stratula, “Numerical modeling of a low-velocity microparticle's spraying process in a heated gas stream”, J. Phys.: Conf. Ser., 1203 (2019), 012021
Nikolay G. Burago, Alexander D. Nikitin, Ilia S. Nikitin, Smart Innovation, Systems and Technologies, 133, Smart Modeling for Engineering Systems, 2019, 185
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
N. G. Burago, I. S. Nikitin, “Algoritmy skvoznogo scheta dlya protsessov razrusheniya”, Kompyuternye issledovaniya i modelirovanie, 10:5 (2018), 645–666
N. G. Burago, A. B. Zhuravlev, I. S. Nikitin, “Continuum model and method of calculating for dynamics of inelastic layered medium”, Math. Models Comput. Simul., 11:3 (2019), 488–498
N. G. Burago, I. S. Nikitin, “Matrix-free conjugate gradient implementation of implicit schemes”, Comput. Math. Math. Phys., 58:8 (2018), 1247–1258
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

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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