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Exact solutions of Euler equations of ideal gasdynamics via Lie group analysis

DSpace at IIT Bombay

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Title Exact solutions of Euler equations of ideal gasdynamics via Lie group analysis
 
Creator SHARMA, VD
RADHA, R
 
Subject substitution principles
gas-dynamics
35l50
35l60
75l05
76m60
gasdynamic euler equations
quasilinear system of pdes
lie group method
shock waves
blast wave
 
Description In this paper, we explicitly characterize a class of solutions to the first order quasilinear system of partial differential equations (PDEs), governing one dimensional unsteady planar and radially symmetric flows of an adiabatic gas involving shock waves. For this, Lie group analysis is used to identify a finite number of generators that leave the given system of PDEs invariant. Out of these generators, two commuting generators are constructed involving some arbitrary constants. With the help of canonical variables associated with these two generators, the assigned system of PDEs is reduced to an autonomous system, whose simple solutions provide non trivial solutions of the original system. It is interesting to remark that one of the special solutions obtained here, using this approach, is precisely the blast wave solution known in the literature.
 
Publisher BIRKHAUSER VERLAG AG
 
Date 2011-07-19T01:21:34Z
2011-12-26T12:50:56Z
2011-12-27T05:37:09Z
2011-07-19T01:21:34Z
2011-12-26T12:50:56Z
2011-12-27T05:37:09Z
2008
 
Type Article
 
Identifier ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK, 59(6), 1029-1038
0044-2275
http://dx.doi.org/10.1007/s00033-007-6140-9
http://dspace.library.iitb.ac.in/xmlui/handle/10054/5130
http://hdl.handle.net/10054/5130
 
Language en