Development of an Improved Gas-Kinetic BGK Scheme for Inviscid and Viscous Flows

This paper deals with the development of an improved gas-kinetic BGK scheme for inviscid and viscous flow fields. As the first step toward efficient calculation, particle distribution functions in the general solution of the BGK model are simplified to the extent that the essential features of the standard gas-kinetic BGK scheme are not lost. Then, improved schemes are suggested, which overcome difficulties that may arise in the applications of BGK-type schemes to compressible viscous flow calculations. A Prandtl number correction method is also developed to allow the present schemes to work for arbitrary Pr number. For steady state problems, convergence acceleration techniques suitable for the present schemes are developed in the framework of an implicit time integration. Various numerical experiments ranging from one-dimensional shock tubes to viscous turbulent flows are performed to demonstrate accuracy, robustness, and other essential features of the present method.