Exact (1+1)-dimensional solutions of discrete planar velocity Boltzmann models

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.