Gas-kinetic relaxation (BGK-Type) schemes for the compressible Euler equations

Starting from the gas-kinetic model, a new class of relaxation schemes for the Euler equations are presented. Instead of linerizing the Euler equations into a few simple waves, the new flow solvers are based on the BGK model for the evolution of particle distribution functions, i.e. a nonequilibrium state will evolve into an equilibrium state along with the increasing of entropy. The numerical discretization combines naturally both the Lax-Wendroff and the Flux Vector Splitting type schemes. The numerical results for a few welldefined test cases are presented to indicate the robustness and accuracy of the BGK-type schemes.