Development of Gas-Kinetic BGK Scheme for Two-Dimensional Compressible Inviscid Flows

Abstract

In this paper, a gas-kinetic scheme based on the BGK (Bhatnagar-Gross-Krook) model is developed for the two-dimensional compressible inviscid flow fields. BGK scheme is an approximate Riemann solver that uses the collisional Boltzmann equation as the governing equation for flow evolutions. For efficient computations, particle distribution functions in the general solution of the BGK model are simplified and used for the flow simulations. High order accuracy is achieved via the reconstruction of flow variables using the MUSCL (Monotone Upstream-Centered Schemes for Conservation Laws) interpolation technique. For steady state problems, an implicit time integration method is adopted here which is more preferable to a multi-stage Runge-Kutta method. To investigate the computational characteristics of BGK scheme in detail, it has been applied to two typical two-dimensional numerical experiments namely, a supersonic wedge and a channel with ramp. The results, compared with some typical schemes like those Steger-Warming (SW) FVS (Flux Vector Splitting), and Roe FDS (Flux Difference Splitting) and available exact solutions are summarized as follows; robust, accurate and high resolution at discontinuities such as shock waves.