Symmetry groups and similarity solutions for the system of equations for a viscous compressible fluid |
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Authors: | Manoj Pandey B.D. Pandey V.D. Sharma |
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Affiliation: | aDepartment of Mathematics, Indian Institute of Technology Bombay, Powai, Mumbai 400 076, India;bDepartment of Mathematics, Ohio State University, Marion, OH 43302, USA |
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Abstract: | Here, using Lie group transformations, we consider the problem of finding similarity solutions to the system of partial differential equations (PDEs) governing one-dimensional unsteady motion of a compressible fluid in the presence of viscosity and thermal conduction, using the general form of the equation of state. The symmetry groups admitted by the governing system of PDEs are obtained, and the complete Lie algebra of infinitesimal symmetries is established. Indeed, with the use of the entailed similarity solution the problem is transformed to a system of ordinary differential equations(ODEs), which in general is nonlinear; in some cases, it is possible to solve these ODEs to determine some special exact solutions. |
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Keywords: | Similarity solutions Lie group analysis Viscous compressible fluids Exact solutions |
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