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. © 2007 American Institute of Physics. DOI: 10.1063/1.2723156