Large size planar discrete velocity models for gas mixtures

We present results for the construction of physically acceptable large size planar discrete velocity models (DVMs), with momenta tiling all integer coordinates of the plane, for binary gas mixtures. We want, with binary collisions, five conservation laws (four for the restriction along one axis): only one for the light mass species with mass m = 1, only one for the heavy mass species with mass M > 1, only two for the momenta along the x, y axes and one for the energy. We restrict our study to models with one zero momentum, while the momenta in the plane are different and occupy only integer coordinates. We start with a preliminary simple physical model satisfying the above constraints and add, with geometrical tools, new momenta. As an illustration we construct models, for M = 2, 3, 4, 5, with an arbitrary number of moments and which occupy all integer coordinates of the plane.