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An extension of the lattice Boltzmann BGK method to compressible flows is presented that combines three novel additions: (1) particles move density and energy weights in multiple velocity bins (11 for 1-D flow) to nearby cell centers. (2) the equilibrium distribution remains an unexpanded Maxwellian; and (3) transport and relaxation to equilibrium are performed implicitly at each node. These advances allow for the parallel modeling of high Mach number shocks and high Reynolds number flows, while avoiding advective numerical diffusion, the need for Riemann solvers, and non-linear limiters. A 1D shock tube application is shown. Generalization to higher dimensions and multi-materials are discussed.