ISSN 2658–5782

DOI 10.21662

DOI 10.21662

Electronic Scientific Journal

2023. Vol. 18. Issue 1, Pp. 9–16

URL: http://mfs.uimech.org/mfs2023.1.002,en

DOI: 10.21662/mfs2023.1.002

URL: http://mfs.uimech.org/mfs2023.1.002,en

DOI: 10.21662/mfs2023.1.002

Collapsing motions of a diatomic gas whose density depends only on time

Gumerov I.I.^{∗}, Katashova A.A.^{∗}, Yulmukhametova Y.V.^{∗∗}

One submodel of gas motion with a linear velocity field is considered in the paper. Namely, a submodel that defines
the movements of a polytropic gas with a density that depends only on time. A polytropic gas is a gas for which
the internal energy is a function linear in temperature. The submodel under consideration is given by a system of
ordinary differential equations of the 22nd order for unknown functions. These functions characterize the movements
of gas particles and determine the type of density, pressure and entropy functions. The exact solution is sought for a
special case, namely for a diagonal linearity matrix. Two new exact solutions have been found. The type of vector
functions of velocity, density and pressure are determined. By the form of the velocity function, the world lines of
motion of gas particles are recorded. In the three-dimensional space of coordinates

polytropic gas,

diatomic gas,

linear velocity field,

inhomogeneous deformation,

trajectories of gas particles,

world lines of particle motion,

Jacobian

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

Methods: The following approach was chosen to find new exact solutions. The linearity matrix is selected in a diagonal form with several identical 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 allowed us to determine the type of all gas-dynamic functions. Velocity, density, pressure and entropy.

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