  A new kinetic model is proposed where the equilibrium distribution with
bounded support has a range of velocities about two average velocities in 1D.
In 2D, the equilibrium distribution function has a range of velocities about
four average velocities, one in each quadrant. In the associated finite volume
scheme, the average velocities are used to enforce the Rankine-Hugoniot jump
conditions for the numerical diffusion at cell-interfaces, thereby capturing
steady discontinuities exactly. The variable range of velocities is used to
provide additional diffusion in smooth regions. Further, a novel kinetic theory
based expression for relative entropy is presented which, along with an
additional criterion, is used to identify expansions and smooth flow regions.
Appropriate flow tangency and far-field boundary conditions are formulated for
the proposed kinetic model. Several benchmark 1D and 2D compressible flow test
cases are solved to demonstrate the efficacy of the proposed solver.
