Modern Methods of Mathematical Modeling of the Development of Hydrodynamic Instabilities and Turbulent Mixing

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 in vari...

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Published inMathematical models and computer simulations Vol. 13; no. 2; pp. 311 - 327
Main Authors Tishkin, V. F., Gasilov, V. A., Zmitrenko, N. V., Kuchugov, P. A., Ladonkina, M. E., Poveschenko, Y. A.
Format Journal Article
LanguageEnglish
Published Moscow Pleiades Publishing 01.03.2021
Springer Nature B.V
Subjects
Computational fluid dynamics
Mathematical analysis
Mathematical Modeling and Industrial Mathematics
Mathematical models
Mathematics
Mathematics and Statistics
Numerical methods
Perturbation
Simulation and Modeling
Three dimensional analysis
Turbulence
Turbulent mixing
Two dimensional analysis
hydrodynamic instabilities
mathematical modeling
accurate numerical methods
turbulent mixing
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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 in various fields of science and engineering. In addition, it should be noted that studies of the characteristics of turbulent flows, for example, have still not been completed. This is inspiring a great deal of interest in this topic, both in the sense of physical theory and in the sense of developing new approaches to the mathematical modeling of the corresponding problems. The capabilities of modern computer technology make it possible to carry out numerical experiments in two-dimensional and three-dimensional setups and analyze the features of the new numerical methods. Presently, numerous methods with many modifications are used in practice. This review focuses on the most promising among them.
AbstractList 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 in various fields of science and engineering. In addition, it should be noted that studies of the characteristics of turbulent flows, for example, have still not been completed. This is inspiring a great deal of interest in this topic, both in the sense of physical theory and in the sense of developing new approaches to the mathematical modeling of the corresponding problems. The capabilities of modern computer technology make it possible to carry out numerical experiments in two-dimensional and three-dimensional setups and analyze the features of the new numerical methods. Presently, numerous methods with many modifications are used in practice. This review focuses on the most promising among them.
Author Zmitrenko, N. V.
Gasilov, V. A.
Tishkin, V. F.
Kuchugov, P. A.
Ladonkina, M. E.
Poveschenko, Y. A.
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– sequence: 2
  givenname: V. A.
  surname: Gasilov
  fullname: Gasilov, V. A.
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  surname: Zmitrenko
  fullname: Zmitrenko, N. V.
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  givenname: P. A.
  surname: Kuchugov
  fullname: Kuchugov, P. A.
  organization: Keldysh Institute for Applied Mathematics, Russian Academy of Sciences
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  surname: Ladonkina
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  surname: Poveschenko
  fullname: Poveschenko, Y. A.
  organization: Keldysh Institute for Applied Mathematics, Russian Academy of Sciences
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Copyright Pleiades Publishing, Ltd. 2021. ISSN 2070-0482, Mathematical Models and Computer Simulations, 2021, Vol. 13, No. 2, pp. 311–327. © Pleiades Publishing, Ltd., 2021. Russian Text © The Author(s), 2020, published in Matematicheskoe Modelirovanie, 2020, Vol. 32, No. 8, pp. 57–90.
Copyright_xml – notice: Pleiades Publishing, Ltd. 2021. ISSN 2070-0482, Mathematical Models and Computer Simulations, 2021, Vol. 13, No. 2, pp. 311–327. © Pleiades Publishing, Ltd., 2021. Russian Text © The Author(s), 2020, published in Matematicheskoe Modelirovanie, 2020, Vol. 32, No. 8, pp. 57–90.
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Snippet The study of the development of perturbations under the influence of various hydrodynamic instabilities, as well as the transition to turbulent mixing and...
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SubjectTerms Computational fluid dynamics
Mathematical analysis
Mathematical Modeling and Industrial Mathematics
Mathematical models
Mathematics
Mathematics and Statistics
Numerical methods
Perturbation
Simulation and Modeling
Three dimensional analysis
Turbulence
Turbulent mixing
Two dimensional analysis
Title Modern Methods of Mathematical Modeling of the Development of Hydrodynamic Instabilities and Turbulent Mixing
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