In the first part, we are going to introduce
the gas-kinetic BGK scheme based on the approximate Boltzmann equation for the numerical solution of the compressible Navier-Stokes equations. The application of the scheme includes viscous flow computation from the low Mach number to hypersonic viscous and heat conduction flows. In the second part, a generalized solution of the kinetic model will be constructed and used to the study of highly nonequilibrium flow, where the Navier-Stokes equations are not valid. The examples include the flow inside the micro-channels, and the shock structure for monatomic and diatomic gases. In the third part, the extension of the kinetic scheme to the complex flow system, such as MHD and multicomponent flow will be discussed.
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