Development of an improved gas-kinetic BGK scheme for inviscid and viscousflows

This paper deals with the development of an improved gas-kinetic BGK scheme for inviscid and viscous Row fields. As the first step toward efficient ca lculation, particle distribution functions in the general solution of the B GK model are simplified to the extent that the essential features of the st andard gas-kinetic BGK scheme are not lost. Then, improved schemes are sugg ested, which overcome difficulties that may arise in the applications of BG K-type schemes to compressible viscous flow calculations. A Prandtl number correction method is also developed to allow the present schemes to work fo r 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 fro m one-dimensional shock tubes to viscous turbulent flows are performed to d emonstrate accuracy, robustness, and other essential features of the presen t method. (C) 2000 Academic Press.