  A low diffusive flux difference splitting based kinetic scheme is developed
based on a discrete velocity Boltzmann equation, with a novel three velocity
model. While two discrete velocities are used for upwinding, the third discrete
velocity is utilized to introduce appropriate additional numerical diffusion
only in the expansion regions, identified using relative entropy
(Kullback-Liebler divergence) at the cell-interface, along with the estimation
of physical entropy. This strategy provides an interesting alternative to
entropy fix, which is typically needed for low diffusive schemes. Grid-aligned
steady discontinuities are captured exactly by fixing the primary numerical
diffusion such that flux equivalence leads to zero numerical diffusion across
discontinuities. Results for bench-mark test problems are presented for
inviscid and viscous compressible flows.
