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Dynamics of shock waves in media with longitudinal stratification. The precise evolutionтезисы доклада
- Автор: Богданов А.Н.
- Сборник: Analytical and Numerical Methodsin Differential Equations (Yanenko 100 and ANMDE 2021)
- Тезисы
- Год издания: 2021
- Место издания: Suranaree University of Technology Nakhon Ratchasima, Thailand
- Первая страница: 11
- Аннотация: The study of the dynamics of shock waves (SW) in inhomogeneous gaseous media is one of thetopical problems in connection with applications [1]. Problem statements of this kind are a natural development of classical studies on the dynamics of shock waves in a homogeneous medium [2].Chiznell is considered the first in this direction [3]. The complexity of the study of these problems in the general case initially determined the way to search for their particular solutions under certain kind of conditions. For some types of density stratification ahead of the SW front, self-similar solutions were obtained: Sakurai [4] investigated such solutions in the case of a power-law density change; for an exponential decrease in density, self-similar solutions were constructed by Hayes [5]. Plane, axisymmetric, and spherical shock waves in a gas of variable density varying according to a power law in the direction of wave motion were investigated in self-similar regimes by F.L. Chernousko [6]. The propagation of hydrocarbons in a gaseous medium with an exponential density distribution was investigated by A.S. Kompaneets [7]. A very original mathematical approach to the problem of propagation of a one-dimensional shock wave in a quiescent polytropic gas with a given, one-dimensional, pressure distribution was presented by L.V. Ovsyannikov [8]. An overview of the achievements made by the end of the 1970s and the presentation of his own original results in this area is devoted to Ch. 8 of the monograph by J. Whitham [9]. Although Whitham’s results were quite close to [4] and [5], the originality of the method for obtaining the dependence of the perturbation rate on the parameters of the medium left questions (acknowledged by the author [9]) about the validity of the results obtained. Numerical calculations of the motion of shock waves in an inhomogeneous medium were carried out in [10]. Cases of the passage of a hydrocarbon layer of constant increased or decreased density and temperature at constant pressure, as well as a different molecular weight and adiabatic exponent, were considered. The results were presented inthe form of graphs, analytical dependences for them were not displayed. An analytical approachto the study of shock waves in inhomogeneous media was proposed [11] by the author of this work, the results obtained in this and other ways in their development are presented in the report.Asymptotic methods are very flexible, acting decisively, one can get an answer of a rathercomplex problem - this rule was perceived by the author through O.S. Ryzhov.
- Добавил в систему: Богданов Андрей Николаевич