An implicit gas kinetic BGK scheme for high temperature equilibrium gas flows on unstructured meshes

Abstract

This paper presents an extension of the gas kinetic BGK scheme to simulate inviscous high temperature equilibrium gas flows on unstructured meshes. In the present scheme, the internal degree of freedom of the gas distribution function is variable according to an effective γ, which is obtained through polynomial curve fits of thermodynamic properties of high temperature equilibrium air. With this method, the proper Euler equations for high temperature equilibrium airflows are recovered from the Boltzmann BGK equation. To accelerate the convergence of the present scheme, the matrix-free LU-SGS implicit time marching scheme is also developed. In addition,for demonstrating the effectiveness and accuracy of the present method, several inviscous airflow examples are also provided. The numerical results agree well with the results of previous studies and show that the present scheme is accurate and robust.