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DOI 10.21662
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Yulmukhametova Yu.V. Deformation of a gas ball into a needle or disk. Multiphase Systems. 19 (2024) 2. 59–63 (in Russian).
2024. Vol. 19. Issue 2, Pp. 59–63
URL: http://mfs.uimech.org/mfs2024.2.009,en
DOI: 10.21662/mfs2024.2.009
Deformation of a gas ball into a needle or disk
Yu.V. Yulmukhametova
Ufa University of Science and Technology, Ufa, Russia,
Mavlyutov Institute of Mechanics UFRC RAS, Ufa, Russia

Abstract

One model of gas motion is considered, the particle velocities of which linearly depend on spatial coordinates. The model consists of two first-order matrix differential equations, two first-order vector differential equations, a gas equation of state and a density function. An exact solution for the antidiagonal linearity matrix has been found for this model. All components of the velocity vector have been determined. The equations of the world lines of motion of gas particles are written down. The motion of the isolated volume of gas particles is investigated.

Keywords

linear velocity field,
uniform deformation,
gas dynamics,
exact solution

Article outline

Objective: to find and study new exact solutions to the equations of ideal gas dynamics with a linear velocity field.

Methods: the following approach was chosen to find new accurate solutions. The linearity matrix is chosen in an anti-diagonal form with various elements. After substituting such a solution into the ordinary differential equations of the model, the form of these matrix elements is determined.

Result: The type of the linearity matrix made it possible to determine the type of all gas dynamic functions. Speed, density and pressure. The equations of the world lines of gas particles are found. The movement of the allocated volume is constructed.

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