  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.
