一个三维多松弛时间全速域格子Boltzmann模型  

A Three-dimensional Multiple-Relaxation-Time Lattice Boltzmann Method for Whole-Speed-Range

作　　者：陈锋 许爱国[2,3] 张广财[2] 焦培刚[1] CHEN Feng;XU Aiguo;ZHANG Guangcai;JIAO Peigang(Shandong Jiaotong University,Jinan 250357,China;National Key Laboratory of Computational Physics,Institute of Applied Physics and Computational Mathematics,Beijing 100088,China;Center for Applied Physics and Technology,MOE Key Center for High Energy Density Physics Simulations,College of Engineering,Peking University,Beijing 100871,China)

机构地区：[1]山东交通学院,济南250357 [2]北京应用物理与计算数学研究所计算物理国家重点实验室,北京100088 [3]北京大学应用物理与技术研究中心和高能量密度物理数值模拟教育部重点实验室,北京100871

出　　处：《计算物理》2018年第4期379-387,共9页Chinese Journal of Computational Physics

基　　金：国家自然科学基金(11402138,11475028,11772064);计算物理重点实验室基金资助项目

摘　　要：构建一个既适用于低速不可压流体又适用于高速可压缩流体的三维自由参数多松弛时间格子Boltzmann模型.模型中,根据SO（3）群的不可约表述基函数构造转化矩阵,根据恢复可压Navier-Stokes方程的需要选取非守恒矩平衡值.通过von Neumann稳定性分析模型参数对数值稳定性的影响,并给出建议选择范围.模型经过基准问题的验证,模拟结果与解析解及其它数值结果符合较好.A three-dimensional（ 3 D） free-parameter multiple-relaxation-time lattice Boltzmann method for high speed compressible and low speed incompressible flows is presented. In the approach transformation matrix is constructed according to irreducible representation basis functions of SO（ 3） group. Equilibria of nonconserved moments are chosen so as to recover compressible NavierStokes equations through Chapman-Enskog analysis. Sizes of discrete velocities are flexible. Influence of model parameters on numerical stability is analyzed. Reference values of parameters are suggested. To validate performance of the model,several wellknown benchmark problems ranging from 1 D to 3 D are simulated. Numerical results are in good agreement with analytical solutions and/or other numerical results.

关 键 词：格子BOLTZMANN 可压缩流体 多松弛时间 

分 类 号：O35[理学—流体力学]