Shock structure in a nine-velocity gas

Details Shock structure in a nine-velocity gas Shock structure in a nine-velocity gas

1995-01-22

arxiv.org/abs/comp-gas/9501008v2

Physica D 73 (1994) 205-216

Nonlinear Sciences

Cellular Automata and Lattice Gases

16 pages including 4 figures and 1 table. All in one postscript file (shck.ps). Compressed and uuencoded (shck.uu). Name mail

Scientific paper

10.1016/0167-2789(94)90157-0

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.

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