Analysis of Discrete Velocity Models for Lattice Boltzmann Simulations of Compressible Flows at Arbitrary Specific Heat Ratio

Abstract

This paper is devoted to the comparison of discrete velocity models used for simulation of compressible flows with arbitrary specific heat ratios in the lattice Boltzmann method. The stability of the governing equations is analyzed for the steady flow regime. A technique for the construction of stability domains in parametric space based on the analysis of eigenvalues is proposed. A comparison of stability domains for different models is performed. It is demonstrated that the maximum value of macrovelocity, which defines instability initiation, is dependent on the values of relaxation time, and plots of this dependence are constructed. For double-distribution-function models, it is demonstrated that the value of the Prantdl number does not seriously affect stability. The off-lattice parametric finite-difference scheme is proposed for the practical realization of the considered kinetic models. The Riemann problems and the problem of Kelvin–Helmholtz instability simulation are numerically solved. It is demonstrated that different models lead to close numerical results. The proposed technique of stability investigation can be used as an effective tool for the theoretical comparison of different kinetic models used in applications of the lattice Boltzmann method.