A simplified circular function-based gas kinetic scheme for simulation of incompressible flows

Abstract

In this paper, the circular function–based gas kinetic scheme (GKS), which is often applied for simulation of compressible flows, is simplified to improve computational efficiency for simulation of incompressible flows. In the original circular function–based GKS, the integral domain along the circle for computing conservative variables and numerical fluxes is usually not symmetric at the cell interface. This leads to relatively complicated formulations for computing the numerical flux at the cell interface. As shown in this work, for incompressible flows, the circle at the cell interface can be approximately considered to be symmetric. As a consequence, the simple expressions for calculation of conservative variables and numerical fluxes at the cell interface can be obtained, and computational efficiency is greatly improved. In the meanwhile, like the original circular function–based GKS, the discontinuity of conservative variables and their derivatives at the cell interface is still kept in the present scheme to keep good numerical stability at high Reynolds numbers. Several numerical examples, including decaying vortex flow, lid-driven cavity flow, and flow past a stationary and rotating circular cylinder, are tested to validate the accuracy, efficiency, and stability of the present scheme. Copyright © 2017 John Wiley & Sons, Ltd.