V. A. Titarev, S. V. Utyuzhnikov, A. V. Chikitkin, “OpenMP + MPI parallel implementation of a numerical method for solving a kinetic equation”, Zh. Vychisl. Mat. Mat. Fiz., 56:11 (2016), 1949–1959; Comput. Math. Math. Phys., 56:11 (2016), 1919

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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2016, Volume 56, Number 11, Pages 1949–1959
DOI: https://doi.org/10.7868/S0044466916110144 (Mi zvmmf10479)

This article is cited in 18 scientific papers (total in 18 papers)

OpenMP + MPI parallel implementation of a numerical method for solving a kinetic equation

V. A. Titarev^ab, S. V. Utyuzhnikov^ac, A. V. Chikitkin^a

^a Moscow Institute of Physics and Technology, Dolgoprudnyi, Moscow oblast, Russia
^b Dorodnicyn Computing Center, Federal Research Center "Computer Science and Control", Russian Academy of Sciences, Moscow, Russia
^c University of Manchester, Manchester, UK

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DOI: https://doi.org/10.7868/S0044466916110144

Abstract: A two-level OpenMP + MPI parallel implementation is used to numerically solve a model kinetic equation for problems with complex three-dimensional geometry. The scalability and robustness of the method are demonstrated by computing the classical gas flow through a circular pipe of finite length and the flow past a reentry vehicle model. It is shown that the two-level model significantly speeds up the computations and improves the scalability of the method.

Key words: S-model, computational rarefied gas dynamics, unstructured mesh, implicit TVD scheme, OpenMP, MPI, supercomputer computations.

Funding agency	Grant number
Russian Foundation for Basic Research	15-01-07911_а 15-07-02986_a
Ministry of Education and Science of the Russian Federation	11.G34.31.0072

Received: 06.08.2015
Revised: 05.10.2015

English version:
Computational Mathematics and Mathematical Physics, 2016, Volume 56, Issue 11, Pages 1919–1928
DOI: https://doi.org/10.1134/S0965542516110129

Bibliographic databases:

Document Type: Article

UDC: 519.634

Language: Russian

Citation: V. A. Titarev, S. V. Utyuzhnikov, A. V. Chikitkin, “OpenMP + MPI parallel implementation of a numerical method for solving a kinetic equation”, Zh. Vychisl. Mat. Mat. Fiz., 56:11 (2016), 1949–1959; Comput. Math. Math. Phys., 56:11 (2016), 1919–1928

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Linking options:

https://www.mathnet.ru/eng/zvmmf10479

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This publication is cited in the following 18 articles:

A. A. Morozov, V. A. Titarev, “Evolution of the shape of a gas cloud during pulsed laser evaporation into vacuum: Direct simulation Monte Carlo and the solution of a model equation”, Comput. Math. Math. Phys., 63:12 (2023), 2244–2256
I. V. Voronich, V. A. Titarev, “Numerical analysis of rarefied gas flow through a system of short channels”, Comput. Math. Math. Phys., 63:12 (2023), 2227–2243
V.A. Titarev, A.A. Morozov, “Arbitrary Lagrangian-Eulerian discrete velocity method with application to laser-induced plume expansion”, Applied Mathematics and Computation, 429 (2022), 127241
A. V. Chikitkin, E. K. Kornev, V. A. Titarev, “Numerical solution of the Boltzmann equation with s-model collision integral using tensor decompositions”, Comput. Phys. Commun., 264 (2021), 107954
Aleksandr V. Chikitkin, Egor K. Kornev, Smart Innovation, Systems and Technologies, 215, Smart Modelling for Engineering Systems, 2021, 105
V. A. Titarev, A. A. Frolova, V. A. Rykov, P. V. Vashchenkov, A. A. Shevyrin, Y. A. Bondar, “Comparison of the Shakhov kinetic equation and DSMC method as applied to space vehicle aerothermodynamics”, J. Comput. Appl. Math., 364 (2020), UNSP 112354
V. A. Titarev, E. M. Shakhov, “A hybrid method for the computation of a rarefied gas jet efflux through a very long channel into vacuum”, Comput. Math. Math. Phys., 60:11 (2020), 1936–1949
Vladimir A. Titarev, Continuum Mechanics, Applied Mathematics and Scientific Computing: Godunov's Legacy, 2020, 353
Egor Kornev, Aleksandr Chikitkin, PROCEEDINGS OF THE X ALL-RUSSIAN CONFERENCE “Actual Problems of Applied Mathematics and Mechanics” with International Participation, Dedicated to the Memory of Academician A.F. Sidorov and 100th Anniversary of UrFU: AFSID-2020, 2312, PROCEEDINGS OF THE X ALL-RUSSIAN CONFERENCE “Actual Problems of Applied Mathematics and Mechanics” with International Participation, Dedicated to the Memory of Academician A.F. Sidorov and 100th Anniversary of UrFU: AFSID-2020, 2020, 050009
Minh Tuan Ho, L. Zhu, L. Wu, P. Wang, Zh. Guo, Zh.-H. Li, Y. Zhang, “A multi-level parallel solver for rarefied gas flows in porous media”, Comput. Phys. Commun., 234 (2019), 14–25
L. M. Yang, C. Shu, W. M. Yang, J. Wu, “An improved three-dimensional implicit discrete velocity method on unstructured meshes for all Knudsen number flows”, J. Comput. Phys., 396 (2019), 738–760
G. Dimarco, R. Loubere, J. Narski, T. Rey, “An efficient numerical method for solving the Boltzmann equation in multidimensions”, J. Comput. Phys., 353 (2018), 46–81
V. A. Titarev, E. M. Shakhov, “Unsteady rarefied gas flow with shock wave in a channel”, Fluid Dyn., 53:1 (2018), 143–151
V. A. Titarev, “Application of model kinetic equations to hypersonic rarefied gas flows”, Comput. Fluids, 169, SI (2018), 62–70
O. V. Ilyin, “A method for simulating the dynamics of rarefied gas based on lattice Boltzmann equations and the BGK equation”, Comput. Math. Math. Phys., 58:11 (2018), 1817–1827
Titarev V.A., Faranosov G.A., Chernyshev S.A., Batrakov A.S., “Numerical Modeling of the Influence of the Relative Positions of a Propeller and Pylon on Turboprop Aircraft Noise”, Acoust. Phys., 64:6 (2018), 760–773
V. A. Titarev, “Numerical modeling of high-speed rarefied gas flows over blunt bodies using model kinetic equations”, Eur. J. Mech. B-Fluids, 64:SI (2017), 112–117
M. N. Petrov, V. A. Titarev, S. V. Utyuzhnikov, A. V. Chikitkin, “A multithreaded OpenMP implementation of the LU-SGS method using the multilevel decomposition of the unstructured computational mesh”, Comput. Math. Math. Phys., 57:11 (2017), 1856–1865

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

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