On the Reduction of the Magnetic Gas Dynamics System of Equations to Systems of Ordinary Differential Equations
https://doi.org/10.56304/S2304487X22020122
Abstract
A magnetic gas dynamics system of equations including the magnetic viscosity is considered. To study this system, systems of partial differential equations is reduced to systems of ordinary differential equations using two approaches. In the first approach, the independent variable $\psi$ of systems of ordinary differential equations is such that the equation ψ(x, y, z, t) = const defines the level surface of the solutions of the original system (components of the velocity vector and components of the magnetic field strength). In the second approach, irrotational motions of plasma are considered, in which the components of the velocity are derivatives of some function Q = Q(x, y, z, t). In this case, the equation ψ(x, y, z, t) = const defines the level surface of the function Q = Q(x, y, z, t) and the components of the magnetic field vector. Some exact solutions of the considered system of partial differential equations are found. It is shown that functional arbitrariness is preserved in each of the considered approaches when determining level surfaces. The available functional arbitrariness is used in the problem of location of streamlines of the potential plasma flow and magnetic field lines on a certain surface. An algorithm for obtaining such a surface is described.
About the Authors
O. N. Ul’yanov
Krasovskii Institute of Mathematics and Mechanics, Ural Branch, Russian Academy of Sciences
Russian Federation
Russian Federation
Yekaterinburg, 620108
L. I. Rubina
Krasovskii Institute of Mathematics and Mechanics, Ural Branch, Russian Academy of Sciences
Russian Federation
Russian Federation
Yekaterinburg, 620108
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For citations:
Ul’yanov O.N., Rubina L.I. On the Reduction of the Magnetic Gas Dynamics System of Equations to Systems of Ordinary Differential Equations. Vestnik natsional'nogo issledovatel'skogo yadernogo universiteta "MIFI". 2022;11(2):122–132. (In Russ.) https://doi.org/10.56304/S2304487X22020122
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