CONSERVATION LAWS AND INVARIANT SOLUTIONS IN THE FANNO MODEL FOR TURBULENT COMPRESSIBLE FLOW

被引：19
|
作者：
Anthonyrajah, M. [1 ,2 ]
Mason, D. P. [1 ,2 ]
机构：
[1] Univ Witwatersrand, Ctr Differential Equat Continuum Mech & Applicat, ZA-2050 Wits, South Africa
[2] Univ Witwatersrand, Sch Computat & Appl Math, ZA-2050 Wits, South Africa
来源：
MATHEMATICAL & COMPUTATIONAL APPLICATIONS | 2010年 / 15卷 / 04期
关键词：
Turbulent flow; conservation laws; multiplier method; associated Lie point symmetries; PARTIAL-DIFFERENTIAL EQUATIONS;
D O I：
10.3390/mca15040529
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
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.
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页码：529 / 542
页数：14
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