  In this paper, a comparison of the performance of two high-order finite
volume methods based on the gas-kinetic scheme (GKS) and HLLC fluxes is carried
out in structured rectangular mesh. For both schemes, the fifth-order WENO-AO
reconstruction is adopted to achieve a high-order spatial accuracy. In terms of
temporal discretization, a two-stage fourth-order (S2O4) time marching strategy
is adopted for WENO5-AO-GKS scheme, and the fourth-order Runge-Kutta (RK4)
method is employed for WENO5-AO-HLLC scheme. For the viscous flow computation,
the GKS includes both inviscid and viscous fluxes in the evolution of a single
cell interface gas distribution function. While for the WENO5-AO-HLLC scheme,
the inviscid flux is provided by HLLC Riemann solver, and the viscous flux is
discretized by a sixth-order central difference method. Based on the tests of
forward Mach step and viscous shock tube, both schemes show outstanding shock
capturing property. From the Titarev-Toro and double shear layer tests,
WENO5-AO-GKS scheme seems to have a better resolution than WENO5-AO-HLLC
scheme. Both schemes show excellent robustness in extreme cases, such as the Le
Blanc problem. From the cases of the Noh problem and the compressible isotropic
turbulence, WENO5-AO-GKS scheme shows favorite robustness. In the compressible
isotropic turbulence and three-dimensional Taylor-Green vortex problems,
WENO-AO-GKS can use a CFL number up to 0.5, instead of 0.3 for WENO5-AO-HLLC.
In terms of computational efficiency, WENO5-AO-HLLC scheme is about 27% more
expensive than WENO5-AO-GKS scheme in the two-dimensional viscous flow
problems, but is about 15% faster in the three-dimensional case. Due to the
multi-dimensionality, WENO5-AO-GKS scheme performs better than WENO5-AO-HLLC
scheme in the laminar boundary layer and the double shear layer test.
