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Shock wave structure in a lattice gas

The motion and structure of shock and expansion waves in a simple particle system, a lattice gas and cellular automaton, are determined in an exact computation. Shock wave solutions, also exact, of a continuum description, a model Boltzmann equation, are compared with the lattice results. The comparison demonstrates that, as proved by Caprino et al. [“A derivation of the Broadwell equation,” Commun. Math. Phys. 135, 443 (1991)] only when the lattice processes are stochastic is the model Boltzmann description accurate. In the strongest shock wave, the velocity distribution function is the bimodal function proposed by Mott-Smith.