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Published May 2007 | Published
Journal Article Open

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.

Additional Information

© 2007 American Institute of Physics (Received 14 September 2006; accepted 8 March 2007; published online 3 May 2007) We thank Russel Caflisch for his participation in the initial modeling work and Roddam Narasimha, Anatol Roshko, and John Torczynski for their helpful comments. We especially thank Godfrey Mungal for his suggestions concerning many aspects of the work.

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