A Numerical Study Comparing Kinetic Flux–Vector Splitting for the Navier–Stokes Equations with a Particle Method

Abstract

Numerical solutions based on the method of kinetic flux-vector splitting (KFVS) for the Navier–Stokes equations are compared with results from the direct simulation Monte Carlo method (DSMC) for three problems: an impulsively started piston, which emphasizes heat flux; an impulsively started flat plate, which emphasizes shearing stress; and a plate sliding past a square cavity, or the lid-driven cavity problem, which combines both stress and heat flux. Taking the view that the DSMC method provides the correct physical description near material boundaries, the comparisons which were carried out for the conditions of a slightly rarefied flow show good agreement for temperature slip, velocity slip, and in the prediction of the kinetic split fluxes, verifying the assumptions and the approach taken in the development of the KFVS method.