ANALYSIS AND IMPLEMENTATION OF THE GAS-KINETIC BGK SCHEME FOR COMPUTATIONAL GAS-DYNAMICS

Gas-kinetic schemes based on the BGK model are proposed as an alternat ive evolution model which can cure some of the limitations of current Riemann solvers. To analyse the schemes, simple advection equations ar e reconstructed and solved using the gas-kinetic BGK model. Results fo r gas-dynamic application are also presented. The final flux function derived in this model is a combination of a gas-kinetic Lax-Wendroff f lux of viscous advection equations and kinetic flux vector splitting. These two basic schemes are coupled through a non-linear gas evolution process and it is found that this process always satisfies the entrop y condition. Within the framework of the LED (local extremum diminishi ng) principle that local maxima should not increase and local minima s hould not decrease in interpolating physical quantities, several stand ard limiters are adopted to obtain initial interpolations so as to get higher-order BGK schemes. Comparisons for well-known test cases indic ate that the gas-kinetic BGK scheme is a promising approach in the des ign of numerical schemes for hyperbolic conservation laws. (C) 1997 by John Wiley & Sons, Ltd.