Abstract
For the discrete Boltzmann models [1] (DBM) the velocities take only a finite number of discrete values v i For their exact solutions the building blocks were the classes of self-similar solutions which, for binary collisions, are in general like the Broadwell shock wave, solutions of scalar Riccati equations. All (1 + 1)—dimensional, (2 + 1), 2D, 3D solutions which, up to now, have been constructed are linear combinations of these self-similar solutions and we report the new results found since a previous review paper [2]. However very recent results [3] show that, for DBM, another class of self-similar solutions corresponding to coupled Riccati equations exists also. For the multiple collisions other new classes of self-similar solutions have been found when quaternary and fifth-order collisions are present [3].
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