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Symmetry analysis and exact solutions of magnetogasdynamic equations

DSpace at IIT Bombay

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Title Symmetry analysis and exact solutions of magnetogasdynamic equations
 
Creator PANDEY, M
RADHA, R
SHARMA, VD
 
Subject lie group-analysis
substitution principles
gas-dynamics
shock
wave
 
Description Using the invariance group properties of the governing system of partial differential equations (PDEs), admitting Lie group of point transformations with commuting infinitesimal generators, we obtain exact solutions to the system of PDEs describing one-dimensional unsteady planar and cylindrically symmetric motions in magnetogasdynamics involving shock waves. Some appropriate canonical variables are characterised that transform the equations at hand to an equivalent autonomous form, the constant solutions of which correspond to non-constant solutions of the original system. The governing system of PDEs includes as a special case the Euler's equations of non-isentropic gasdynamics. It is interesting to remark that in the absence of magnetic field, one of the exact solutions obtained here is precisely the blast wave solution obtained earlier using a different method of approach. A particular solution to the governing system, which exhibits space-time dependence, is used to study the wave pattern that finally develops when a magnetoacoustic wave impacts with a shock. The influence of magnetic field strength on the evolutionary behaviour of incident and reflected waves and the jump in shock acceleration, after collision, are studied.
 
Publisher OXFORD UNIV PRESS
 
Date 2011-08-22T07:22:39Z
2011-12-26T12:56:15Z
2011-12-27T05:44:38Z
2011-08-22T07:22:39Z
2011-12-26T12:56:15Z
2011-12-27T05:44:38Z
2008
 
Type Article
 
Identifier QUARTERLY JOURNAL OF MECHANICS AND APPLIED MATHEMATICS, 61(), 291-310
0033-5614
http://dx.doi.org/10.1093/qjmam/hbn011
http://dspace.library.iitb.ac.in/xmlui/handle/10054/10357
http://hdl.handle.net/10054/10357
 
Language en