Conservation laws and invariant solutions in the Fanno model for turbulent compressible flow

Abstract

Asymptotic reductions of the Fanno model for one-dimensional turbu- lent 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 equa- tion for the mean pressure. Two conserved quantities for the mean velocity are obtained from the conservation laws and boundary conditions. An invariant solu- tion 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.