  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.
