In this paper, a switch function-based gas-kinetic scheme (SF-GKS) is presented
for the simulation of inviscid and viscous compressible flows. With the finite
volume discretization, Euler and Navier-Stokes equations are solved and the SF-GKS
is applied to evaluate the inviscid flux at cell interface. The viscous flux is obtained by
the conventional smooth function approximation. Unlike the traditional gas-kinetic
scheme 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 shock
waves. As a consequence, the present SF-GKS can well capture strong shock waves
and thin boundary layers simultaneously. The present SF-GKS is firstly validated by
its application to the inviscid flow problems, including 1-D Euler shock tube, regular
shock reflection and double Mach reflection. Then, SF-GKS is extended to solve viscous
transonic and hypersonic flow problems. Good agreement between the present
results and those in the literature verifies the accuracy and robustness of SF-GKS.