Highly Efficient Lattice Boltzmann Model for Compressible Fluids:Two-Dimensional Case  

作　　者：CHEN Feng XU Ai-Guo ZHANG Guang-Cai GAN Yan-Biao CHENG Tao LI Ying-Jun 

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

出　　处：《Communications in Theoretical Physics》2009年第10期681-693,共13页理论物理通讯（英文版）

基　　金：Supported by the Science Foundations of LCP and CAEP under Grant Nos.2009A0102005 and 2009B0101012;the National Basic Research Program (973 Program) under Grant No.2007CB815105;the National Natural Science Foundation under Grant Nos.10775018,10702010,and 10775088

摘　　要：We present a highly efficient lattice Boltzmann model for simulating compressible flows. This model is based on the combination of an appropriate finite difference scheme, a 16-discrete-velocity model [Kataoka and Tsutahara, Phys. Rev. E 69 （2004） 035701（R）] and reasonable dispersion and dissipation terms. The dispersion term effectively reduces the oscillation at the discontinuity and enhances numerical precision. The dissipation term makes the new model more easily meet with the yon Neumann stability condition. This model works for both high-speed and low-speed flows with arbitrary specific-heat-ratio. With the new model simulation results for the well-known benchmark problems get a high accuracy compared with the analytic or experimental ones. The used benchmark tests include （i） Shock tubes such as the Sod, Lax, Sjogreen, Colella explosion wave, and collision of two strong shocks, （ii） Regular and Mach shock reflections, and （iii） Shock wave reaction on cylindrical bubble problems. With a more realistic equation of state or free-energy functional, the new model has the potential tostudy the complex procedure of shock wave reaction on porous materials.

关 键 词：lattice Boltzmann method compressible flows specific-heat-ratio von Neumann stability analysis 

分 类 号：O35[理学—流体力学] O354[理学—力学]