A Method for Near-Equilibrium Discrete-Velocity Gas Flows

We present a simulation scheme for discrete-velocity gases based on {\em local thermodynamic equilibrium}. Exploiting the kinetic nature of discrete-velocity gases, in that context, results in a natural splitting of fluxes, and the resultant scheme strongly resembles the original processes. The kinetic nature of the scheme and the modeling of the {\em infinite collision rate} limit, result in a small value of the coefficient of (numerical)-viscosity, the behavior of which is remarkably physical [18]. A first order method, and two second order methods using the total variation diminishing principle are developed and an example application presented. Given the same computer resources, it is expected that with this approach, much higher Reynold's number will be achievable than presently possible with either lattice gas automata or lattice Boltzmann approaches. The ideas being general, the scheme is applicable to any discrete-velocity model, and to lattice gases as well.