Finite-Difference Lattice Boltzmann Scheme for High-Speed Compressible Flow:Two-Dimensional Case  

作　　者：GAN Yan-Biao XU Ai-Guo ZHANG Guang-Cai ZHANG Ping ZHANG Lei LI Ying-Jun 

机构地区：[1]China University of Mining and Technology （Beijing）, Beijing 100083, China [2]State Key Laboratory of Computational Physics, Institute of Applied Physics and Computational Mathematics, P.O. Box 8009-26, Beijing 100088, China [3]Fundamental Science Department, North China Institute of Aerospace Engineering, Langfang 065000, China

出　　处：《Communications in Theoretical Physics》2008年第7期201-210,共10页理论物理通讯（英文版）

基　　金：the Science Foundation of Laboratory of Computational Physics,the State Key Basic Research Program (973 Program) under Grant No.2007CB815105;National Natural Science Foundation of China under Grant Nos.10775018,10474137,10702010,and 10604010

摘　　要：Lattice Boltzmann （LB） modeling of high-speed compressible flows has long been attempted by various authors. One common weakness of most of previous models is the instability problem when the Mach number of the flow is large. In this paper we present a finite-difference LB model, which works for flows with flexible ratios of specific heats and a wide range of Mach number, from 0 to 30 or higher. Besides the discrete-velocity-model by Watari [Physica A 382 （2007） 502], a modified Lax Wendroff finite difference scheme and an artificial viscosity are introduced. The combination of the finite-difference scheme and the adding of artificial viscosity must find a balance of numerical stability versus accuracy. The proposed model is validated by recovering results of some well-known benchmark tests： shock tubes and shock reflections. The new model may be used to track shock waves and/or to study the non-equilibrium procedure in the transition between the regular and Mach reflections of shock waves, etc.

关 键 词：lattice Boltzmann method high-speed compressible flow von Neumann analysis 

分 类 号：O41[理学—理论物理]