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

• Published in: Mathematical 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
• Language: English
• 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
• ISSN: 2070-0482; 2070-0490
• DOI: 10.1134/S2070048221020174

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.