A Kinetic Flux Difference Splitting method for compressible flows

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.

Automated summary

A low diffusive flux difference splitting based kinetic scheme is proposed by introducing an additional numerical diffusion using a third velocity in the expansion regions, identified using relative entropy (Kullback-Liebler divergence) and physical entropy estimation. This scheme provides an alternative to entropy fix and captures grid-aligned steady discontinuities exactly. Results of bench-mark test problems for both inviscid and viscous compressible flows are presented.