Abstract:
The study of the development of perturbations under the influence of various hydrodynamic instabilities, as well as the transition to turbulent mixing and turbulence, has been
a subject of considerable interest over the past decades. This is primarily due to the importance of these phenomena for various fields of science and technology. It should be
noted, that the final results of the turbulent flows characteristics study have not yet been
obtained. This fact stimulates a great interest in this topic, both in sense of physical theory and in sense of approaches to mathematical modeling and numerical methods development. The capabilities of modern computer technology make it possible to carry out
numerical experiments in two-dimensional and three-dimensional settings, and to analyze
the features of new numerical methods. To date, there are a huge number of methods and
their modifications are applied in practice. This review is devoted to the most promising,
according to the authors, of them.
Citation:
V. F. Tishkin, V. A. Gasilov, N. V. Zmitrenko, P. A. Kuchugov, M. E. Ladonkina, Yu. A. Poveschenko, “Modern methods of mathematical modeling of the development of hydrodynamic instabilities and turbulent mixing”, Mat. Model., 32:8 (2020), 57–90; Math. Models Comput. Simul., 13:2 (2021), 311–327
\Bibitem{TisGasZmi20}
\by V.~F.~Tishkin, V.~A.~Gasilov, N.~V.~Zmitrenko, P.~A.~Kuchugov, M.~E.~Ladonkina, Yu.~A.~Poveschenko
\paper Modern methods of mathematical modeling of the development of hydrodynamic instabilities and turbulent mixing
\jour Mat. Model.
\yr 2020
\vol 32
\issue 8
\pages 57--90
\mathnet{http://mi.mathnet.ru/mm4206}
\crossref{https://doi.org/10.20948/mm-2020-08-05}
\transl
\jour Math. Models Comput. Simul.
\yr 2021
\vol 13
\issue 2
\pages 311--327
\crossref{https://doi.org/10.1134/S2070048221020174}
Linking options:
https://www.mathnet.ru/eng/mm4206
https://www.mathnet.ru/eng/mm/v32/i8/p57
This publication is cited in the following 6 articles:
Y. A. Kriksin, V. F. Tishkin, “Entropic regularization of the discontinuous Galerkin method in conservative variables for three-dimensional Euler equations”, Math. Models Comput. Simul., 16:6 (2024), 843–852
Elena Protsenko, Aleksandr Strazhko, Sofya Protsenko, PROCEEDING OF THE 7TH INTERNATIONAL CONFERENCE OF SCIENCE, TECHNOLOGY, AND INTERDISCIPLINARY RESEARCH (IC-STAR 2021), 2601, PROCEEDING OF THE 7TH INTERNATIONAL CONFERENCE OF SCIENCE, TECHNOLOGY, AND INTERDISCIPLINARY RESEARCH (IC-STAR 2021), 2023, 040004
K. V. Khishchenko, A. A. Charakhch'yan, “Numerical study of instability of medium interface during thermonuclear combustion of a cylindrical shelled microtarget”, Comput. Math. Math. Phys., 63:4 (2023), 644–658
E. N. Shirokova, “Numerical Study of a Pulsed Jet Flow of an Inhomogeneous Gas-Dispersed Mixture”, Fluid Dyn, 58:8 (2023), 1594
Alexander Sukhinov, Alexander Chistyakov, Inna Kuznetsova, Yulia Belova, Alla Nikitina, “Mathematical Model of Suspended Particles Transport in the Estuary Area, Taking into Account the Aquatic Environment Movement”, Mathematics, 10:16 (2022), 2866
M. D. Bragin, “Influence of monotonization on the spectral resolution of bicompact schemes in the inviscid Taylor–Green vortex problem”, Comput. Math. Math. Phys., 62:4 (2022), 608–623
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