a Study of Multi-Speed Discrete-Velocity Gases

The applicability of multi-speed discrete-velocity gases to compressible flow situations is considered. First, the equation of state, the anisotropies and the advection velocities for any multi-speed model on the square and triangular lattices are derived. The dependence on the model of any of these to leading order in tile flow velocity is shown to be only through a fourth moment of the stationary equilibrium speed distribution. Next, a computation scheme is introduced, wherein adjacent cells in a cell network interact through an exchange of particles, commensurate with the equilibrium fluxes of mass, momentum, and energy. This corresponds to the infinite collision rate limit of the model gas, resulting in very low viscosities. Finally, a simple multi-speed model, the nine-velocity model is studied in detail: Solving the shock tube flow with the model yields almost all phenomenology associated with a perfect gas. An exact shock profile is computed for the model and is compared to a Navier-Stokes shock profile. An adiabatic channel flow is simulated with the model and the results compared to an integral solution of the Navier -Stokes equation. The comparisons in both the cases are excellent. It is also shown that the nine-velocity gas does not permit steady supersonic flow.