Numerical simulation of flow around an airfoil with gas-kinetic BGK scheme

This article presents a method for the numerical solution of compressible viscid and inviscid flow with two dimensional body-fitted grids based on an improved gas-kinetic BGK (Bhatnagaar-Gross-Krook) scheme. This method has been improved in flux computation on a non-uniform grid. In the reconstruction stage, four cells around the cell interface are grouped into one. The macroscopic variables including density, momentum and energy of group cells are transferred to a local coordinate system on the cell interface. The macroscopic variables of the cell interface are interpolated via the van Leer limiter and the fluxes across the cell interface can be computed with the BGK scheme. In this method the computing scheme does not change between the two dimensional body-fitted grids and the uniform grids. The computation load is reduced and the method is simple compared with the other gas-kinetic BGK methods on non-umiform grid. Simulation and research are carried out respectively for a subsonic, transonic and supersonic flow around an airfoil NACA0012. The results of the compressible in viscid flow by the present method agree well with advisory group for aerospace research and development (AGARD) results. The numerical simulation results for a compressible viscid flow agree well with numerical results of references. Thus it is proved that this method has excellent robustness in numerical simulation and shock-capturing aspect. This scheme provides a simple way of calculation for complex flows.