A Kinetic Flux Difference Splitting Method for Compressible Flows

TL;DR

This paper introduces a novel kinetic flux difference splitting method for compressible flows that uses a three velocity model and entropy-based criteria to improve accuracy and stability in capturing discontinuities.

Contribution

It develops a low diffusive kinetic scheme with a three velocity model that adaptively introduces numerical diffusion based on entropy measures, offering an alternative to traditional entropy fixes.

Findings

Accurately captures grid-aligned steady discontinuities

Demonstrates effectiveness on benchmark compressible flow problems

Reduces numerical diffusion in expansion regions

Abstract

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.