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Some special solutions of self similar type in MHD, obtained by a separation method of variables
Published online by Cambridge University Press: 15 August 2002
Abstract
We use a method based on a separation of variables for solving a first order partial differential equations system, using a very simple modelling of MHD. The method consists in introducing three unknown variables Φ1, Φ2, Φ3 in addition to the time variable t and then in searching a solution which is separated with respect to Φ1 and t only. This is allowed by a very simple relation, called a “metric separation equation”, which governs the type of solutions with respect to time. The families of solutions for the system of equations thus obtained, correspond to a radial evolution of the fluid. Solving the MHD equations is then reduced to find the transverse component H∑ of the magnetic field on the unit sphere Σ by solving a non linear partial equation on Σ. Thus, we generalize ideas of Courant-Friedrichs [7] and of Sedov [11], on dimensional analysis and self-similar solutions.
- Type
- Research Article
- Information
- ESAIM: Mathematical Modelling and Numerical Analysis , Volume 33 , Issue 5 , September 1999 , pp. 939 - 963
- Copyright
- © EDP Sciences, SMAI, 1999