  A new discrete-velocity model is presented to solve the three-dimensional
Euler equations. The velocities in the model are of an adaptive nature---both
the origin of the discrete-velocity space and the magnitudes of the
discrete-velocities are dependent on the local flow--- and are used in a finite
volume context. The numerical implementation of the model follows the
near-equilibrium flow method of Nadiga and Pullin [1] and results in a scheme
which is second order in space (in the smooth regions and between first and
second order at discontinuities) and second order in time. (The
three-dimensional code is included.) For one choice of the scaling between the
magnitude of the discrete-velocities and the local internal energy of the flow,
the method reduces to a flux-splitting scheme based on characteristics. As a
preliminary exercise, the result of the Sod shock-tube simulation is compared
to the exact solution.
