Universal Journal of Mechanical Engineering Vol. 7(3), pp. 111 - 117
DOI: 10.13189/ujme.2019.070304
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An Analytical Solution of Dynamics of Self-gravitating Spherical Gas-Dust Cloud

M. Abobaker ^*
Department of Theoretical Mechanics, Peter the Great St. Petersburg Polytechnic University, Russia

ABSTRACT

In this paper, we present a simple model for the dynamics of one dimensional of a self-gravitating spherical symmetrical gas-dust cloud. We take two analytical approaches to study the dynamics of a gravitating system of a gasdust cloud. The first approach solves a set of non-linear equation of dynamics of a gravitating system. The second approach is a Cole-Hopf transformation, which is used to simplify the equations of dynamics and after that, we applied the method of characteristics to reduce partial differential equations to a system of entirely solvable ordinary differential equations. The results found by the analytical method and the Cole-Hopf method are compared with each other, showing that both lead to the same result. The obtained results in this study are presented in plots. We used the Mathematica software package in performing calculation and plotting graphs.

KEYWORDS
Hydrodynamics, Non-linear PDE, Cole-Hopf Method, Gravitating System

Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] M. Abobaker , "An Analytical Solution of Dynamics of Self-gravitating Spherical Gas-Dust Cloud," Universal Journal of Mechanical Engineering, Vol. 7, No. 3, pp. 111 - 117, 2019. DOI: 10.13189/ujme.2019.070304.

(b). APA Format:
M. Abobaker (2019). An Analytical Solution of Dynamics of Self-gravitating Spherical Gas-Dust Cloud. Universal Journal of Mechanical Engineering, 7(3), 111 - 117. DOI: 10.13189/ujme.2019.070304.