AN EULER SOLVER BASED ON LOCALLY ADAPTIVE DISCRETE VELOCITIES

A new discrete-velocity model is presented to solve the three-dimensio nal Euler equations. The velocities in the model are of an adaptive na ture-both the origin of the discrete-velocity space and the magnitudes of the discrete velocities are dependent on the local flow-and are us ed in a finite-volume context. The numerical implementation of the mod el follows the near-equilibrium flow method of Nadiga and Pullin and r esults in a scheme which is second order in space (in the smooth regio ns and between first and second order at discontinuities) and second o rder in time. (The three-dimensional code is included.) For one choice of the scaling between the magnitude of the discrete velocities and t he local internal energy of the flow, the method reduces to a flux-spl itting scheme based on characteristics. As a preliminary exercise, the result of the Sod shock-tube simulation is compared to the exact solu tion.