Half-space large size discrete velocity models

We recall recent large size "physical" discrete velocity models (DVMs) results [1] for a gas in a half-plane (z>0, x being the other coordinate) and present new ones. We consider both single-gas and binary mixtures with light mass 1 and heavy mass M. For the half-space (flow of a semi-infinite expanse of gas in contact with its condensed phase), the interface is located at z=0 with only a z spatial dependence of the gas (densities with (+/-x, z) are equal) and no velocities parallel to the x-axis (or z=0). We construct "physical" DVMs, (only mass, energy and momentum along the z-axis invariants, no spurious invariants), filling all integer coordinates znot equal0 of the plane. The main new result for mixtures, is that we present different M models with the same geometrical structure in the plane with sums of the moduli of the coordinates either odd or even for heavy or light species.