A Switch Function-Based Gas-Kinetic Scheme for Simulation of Inviscid and Viscous Compressible Flows (Advances in Applied Mathematics and Mechanics, 2018)
In this paper, a switch function-based gas-kinetic scheme (SF-GKS) is presentedfor the simulation of inviscid and viscous compressible flows. With the finitevolume discretization, Euler and Navier-Stokes equations are solved and the SF-GKSis applied to evaluate the inviscid flux at cell interface. The viscous flux is obtained bythe conventional smooth function approximation. Unlike the traditional gas-kineticscheme in the calculation of inviscid flux such as Kinetic Flux Vector Splitting (KFVS),the numerical dissipation is controlled with a switch function in the present scheme.That is, the numerical dissipation is only introduced in the region around strong shockwaves. As a consequence, the present SF-GKS can well capture strong shock wavesand thin boundary layers simultaneously. The present SF-GKS is firstly validated byits application to the inviscid flow problems, including 1-D Euler shock tube, regularshock reflection and double Mach reflection. Then, SF-GKS is extended to solve viscoustransonic and hypersonic flow problems. Good agreement between the presentresults and those in the literature verifies the accuracy and robustness of SF-GKS.