Abstract
For discrete velocity Boltzmann models we have found (1+1)-dimensional shock waves and periodic solutions that are rational solutions with two exponential variables exp(γix + ρit) (spacex, timet). These exact solutions are sums of two rational solutions, each with one exponential variable (similarity solutions). We study the planar velocity models and explicitly write the results for the square 4-velocity and the hexagonal 6-velocity models introduced by Gatignol.
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Cornille, H. Exact (1+1)-dimensional solutions of discrete planar velocity Boltzmann models. J Stat Phys 48, 789–811 (1987). https://doi.org/10.1007/BF01019697
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DOI: https://doi.org/10.1007/BF01019697