Multiple-relaxation-time lattice Boltzmann approach to compressible flows with flexible specific-heat ratio and Prandtl number

¹  State Key Laboratory for GeoMechanics and Deep Underground Engineering, China University of Mining and Technology (Beijing) - Beijing 100083, PRC
²  National Key Laboratory of Computational Physics, Institute of Applied Physics and Computational Mathematics P. O. Box 8009-26, Beijing 100088, PRC
³  Istituto Applicazioni Calcolo-CNR - Viale del Policlinico 137, 00161, Roma, Italy, EU

Corresponding author: Xu_Aiguo@iapcm.ac.cn

Received: 30 April 2010
Accepted: 30 May 2010

Abstract

A new multiple-relaxation-time lattice Boltzmann scheme for compressible flows with arbitrary specific-heat ratio and Prandtl number is presented. In the new scheme, which is based on a two-dimensional 16-discrete-velocity model, the kinetic moment space and the corresponding transformation matrix are constructed according to the seven-moment relations associated with the local-equilibrium distribution function. In the continuum limit, the model recovers the compressible Navier-Stokes equations with flexible specific-heat ratio and Prandtl number. Numerical experiments show that compressible flows with strong shocks can be simulated by the present model up to Mach numbers Ma ~ 5.