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Math. Comput. Appl. 2010, 15(4), 529-542; doi:10.3390/mca15040529

Conservation Laws and Invariant Solutions in the Fanno Model for Turbulent Compressible Flow

Centre for Differential Equations, Continuum Mechanics and Applications and School of Computational and Applied Mathematics, University of the Witwatersrand, Johannesburg, Private Bag 3, Wits 2050, South Africa
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Published: 1 December 2010
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Abstract

Asymptotic reductions of the Fanno model for one-dimensional turbulent compressible flow of a perfect gas in a long tube are investigated. Conservation laws are derived using the multiplier method for a nonlinear wave equation and a nonlinear diffusion equation for the mean velocity and a nonlinear diffusion equation for the mean pressure. Two conserved quantities for the mean velocity are obtained from the conservation laws and boundary conditions. An invariant solution is derived for the mean velocity using the Lie point symmetries associated with the conserved vector which generated the conserved quantity for the boundary value problem.
Keywords: Turbulent flow; conservation laws; multiplier method; associated Lie point symmetries Turbulent flow; conservation laws; multiplier method; associated Lie point symmetries
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).

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MDPI and ACS Style

Anthonyrajah, M.; Mason, D. Conservation Laws and Invariant Solutions in the Fanno Model for Turbulent Compressible Flow. Math. Comput. Appl. 2010, 15, 529-542.

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