Shock structure in a nine-velocity gas
Abstract
The exact structure of a shock is computed in a multiple-speed discrete-velocity gas, the nine-velocity gas, wherein the multiplicity of speeds ensures nontrivial thermodynamics. Obtained as a solution of the model Boltzmann equations, the procedure consists of tracking the shock as a trajectory of a three dimensional dynamical system connecting an equilibrium upstream state to an equilibrium downstream state. The two equilibria satisfy the jump conditions obtained from the model Euler equations. Comparison of the shock structure to that in a monatomic perfect gas, as given by the Navier-Stokes equation, shows excellent agreement. The shock in the nine-velocity gas has an overshoot in entropy alone, like in a monatomic gas. The near-equilibrium flow technique for discrete-velocity gases (Nadiga \& Pullin [2]), a kinetic flux-splitting method based on the local thermodynamic equilibrium, is also seen to capture the shock structure remarkably well.
Cite
@article{arxiv.comp-gas/9501008,
title = {Shock structure in a nine-velocity gas},
author = {Balu Nadiga and Brad Sturtevant},
journal= {arXiv preprint arXiv:comp-gas/9501008},
year = {2009}
}
Comments
16 pages including 4 figures and 1 table. All in one postscript file (shck.ps). Compressed and uuencoded (shck.uu). Name mail file `shck.uu'. Edit so that `#!/bin/csh -f' is the first line of shck.uu. On a unix machine say `csh shck.uu'. On a non-unix machine: uudecode adv.uu; uncompress adv.tar.Z; tar -xvf adv.tar