  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.

Fluid Dynamics;Computational Physics