SHOCK STRUCTURE IN A 9-VELOCITY GAS

The exact structure of a shock is computed in a multiple-speed discret e-velocity gas, the nine-velocity gas, wherein the multiplicity of spe eds ensures non-trivial thermodynamics. Obtained as a solution of the model Boltzmann equations, the procedure consists of tracking the shoc k as a trajectory of a three-dimensional dynamical system connecting a n equilibrium upstream state to an equilibrium downstream state. The t wo equilibria satisfy the jump conditions obtained from the model Eule r equations. Comparison of the shock structure to that in a monatomic perfect gas, as given by the Navier-Stokes equation, shows excellent a greement. The shock in the nine-velocity gas has an overshoot in entro py alone, like in a monatomic gas. The near-equilibrium flow technique for discrete-velocity gases [B.T. Nadiga and D.I. Pullin, J. Comp. Ph ys., submitted], a kinetic flux-splitting method based on the local th ermodynamic equilibrium, is also seen to capture the shock structure r emarkably well.