基于多块对接网格的隐式气体运动论统一算法应用研究

彭傲平; 李志辉; 吴俊林; 蒋新宇

doi:10.6052/0459-1879-14-279

基于多块对接网格的隐式气体运动论统一算法应用研究

doi: 10.6052/0459-1879-14-279

1.
中国空气动力研究与发展中心超高速所, 四川绵阳 621000
2. 国家计算流体力学实验室, 北京 100191

基金项目: 国家重点基础研究发展计划(2014CB744100),国家杰出青年科学基金(11325212)和国家自然科学基金(91016027)资助项目.

详细信息

通讯作者:
李志辉,研究员,主要研究方向:跨流域空气动力学.E-mail:zhli0097@x263.net

中图分类号: V211.3
计量
- 文章访问数: 1065
- HTML全文浏览量: 63
- PDF下载量: 998
- 被引次数: 0
出版历程
- 收稿日期: 2014-09-15
- 修回日期: 2015-10-28
- 刊出日期: 2016-01-18

AN APPLICATION OF IMPLICIT GAS-KINETIC UNIFIED ALGORITHM BASED ON MULTIBLOCK PATCHED GRID

1.
Hypervelocity Aerodynamics Institute, China Aerodynamics Research and Development Center, Mianyang 621000, Sichuan, China
2. National Laboratory for Computational Fluid Dynamics, Beijing 100191, China

摘要

摘要: 基于玻尔兹曼模型方程的气体运动论统一算法(gas kinetic unified algorithm,GKUA) 给出了一种能模拟从连续流到自由分子流跨流域空气动力学问题的途径. 该算法采用传统计算流体力学技术将分子运动和碰撞解耦处理,若采用显式格式将受格式稳定条件限制,在模拟超声速流动尤其是近连续流和连续流区的流动时计算效率较低. 为了提高计算效率,扩展其工程实用性,采用上下对称高斯-赛德尔(LU-SGS) 方法和有限体积法构造了求解玻尔兹曼模型方程的隐式方法,同时在物理空间采用能处理任意连接关系的多块对接网格技术. 通过模拟近连续过渡区并排圆柱绕流问题,计算结果与直接模拟蒙特卡洛方法模拟值吻合较好,验证了该方法用于跨流域空气动力计算的可靠性与可行性.
- 气体运动论统一算法 /
- 隐式格式 /
- 多块对接网格 /
- 有限体积法 /
- 跨流域空气动力学
Abstract: Gas Kinetic Unified Algorithm (GKUA) based on Boltzmann model equations is proposed for simulating aerodynamics problems covering various flow regimes. In this algorithm, molecular motions are decoupled from collisions by traditional Computational Fluid Dynamics methods, so that the calculation e ciency would be quite low at the limitation of stabilization conditions of explicit schemes when simulating supersonic flows especially which are near-continuum and continuum flows. In order to improve the e ciency and expand engineering practicability, an implicit method for Boltzmann model equations is constructed by using LU-SGS (Lower-Upper Symmetric Gauss-Seidel) method and cellcentered finite volume method, and multi-block patched grid technique is used in physical space. The present computed results of two side-by-side cylinders in transitional flow regime are found in good agreement with those from Direct simulation Monte-Carlo method simulation. The dependability and feasibility for simulating problems covering various flow regimes by the present method are validated.
- gas-kinetic unified algorithm /
- implicit scheme /
- multi-block patched grid /
- finite volume method /
- aerodynamics covering various flow regimes

HTML全文

参考文献(24)

1 庄逢甘,崔尔杰,张涵信. 未来空间飞行器的某些发展和空气动力学的任务. 中国第一届近代空气动力学与气动热力学会议论文集,2006. 1-12 (Zhuang Fenggan,Cui Erjie,Zhang Hanxin. Some development of future spacecrafts and aerodynamics tasks. In: Proc. of First Aerodynamics and Aerothermodynamics, 2006. 1-12 (in Chinese))

2 李志辉,蒋新宇,吴俊林等. 转动非平衡玻尔兹曼模型方程统一算法与全流域绕流计算应用. 力学学报, 2014, 46(3): 336-351 (Li Zhihui, Jiang Xinyu, Wu Junlin, et al. Gas-kinetic unified algorithm for Boltzmann model equation in rotational non-equilibrium and its application to the whole range flow regimes. Chinese Journal of Theoretical and Applied Mechanics, 2014, 46(3): 336-351 (in Chinese))

3 Chapmann S, Cowling TG. The Mathematical Theory of Non- Uniform Gases, 3rd edn. Cambridge: Cambridge University Press,1970

4 WagnerW. A convergence proof for Bird's Direct Simulation Monte Carlo method for Boltzmann equation. Journal of Statistic Physics,1992, 66: 1011-1044

5 Li ZH, Fang M, Jiang XY, et al. Convergence proof of the DSMC method and the Gas-Kinetic Unified Algorithm for the Boltzmann equation. Sci. China-Phys. Mech. Astron, 2013, 56(2): 404-417

6 Bhatnagar PL,Gross EP,Krook M.A model collision processes in gases:I.Small amplitude processes is charged and neutral onecomponent system.Phys Rev,1954,94:511-525

7 Holway LH. New statistical models for kinetic theory: methods of construction. Phys Fluids, 1966, 9(9): 1658-1673

8 Shakhov EM. Generalization of the krook kinetic relaxation equation. Fluid Dynamics, 1968, 3(5): 95-96

9 Shakhov EM.Kinetic model equations and numerical results.In: Oguchi H. ed.Proceedings of 14th International Symposium on Rarefied Gas Dynamics,Tokyo:University of Tokyo Press,1984.137-148

10 Yang JY, Huang JC. Rarefied flow computations using nonlinear model Boltzmann equations. J of Comput Phys, 1995, 120: 323-339

11 Kudryavtsev AN, Shershnev AA. A numerical method for simulation of microflows by solving directly kinetic equations with WENO schemes. J Sci Comput, 2013, 57: 42-73

12 Mieussens L. Discrete-velocity models and numerical schemes for the Boltzmann-BGK equation in plane and axisymmetric geometries. J of Comput Phys, 2000, 162(2): 429-466

13 Ahn JW, Kim C. An axisymmetric computational model of generalized hydrodynamic theory for rarefied multi-species gas flows. J of Comput Phys, 2009, 228: 4088-4117

14 Xu K, Huang JC. A unified gas-kinetic scheme for continuum and rarefied flows. J Comput Phys, 2010, 229: 7747-7764

15 Xu Kun. A gas-kinetic BGK scheme for the Navier-Stokes equations and its connection with artificial dissipation and godunov method. J of Comput Phys, 2001, 171: 289-335

16 李志辉. 从稀薄流到连续流的气体运动论统一数值算法研究. [博士论文]. 绵阳:中国空气动力研究与发展中心,2001 (Li Zhihui. Study on gas kinetic unified algorithm for flows from rarefied transition to continuum. [PhD Thesis]. Mianyang: China Aerodynamics Research and Development Center, 2001(in Chinese))

17 李志辉, 张涵信. 稀薄流到连续流的气体运动论模型方程算法研究. 力学学报, 2002, 34(2): 145-155 (Li Zhihui, Zhang Hanxin. Study on gas kinetic algorithm for flows from rarefied transition to continuum using Boltzmann model equation. Chinese Journal of Theoretical and Applied Mechanics, 2002, 34(2): 145-155 (in Chinese))

18 Li ZH, Zhang HX. Gas-kinetic numerical studies of threedimensional complex flows on spacecraft re-entry. J Comput Phys,2009, 228: 1116-1138

19 Riabov VV. Aerodynamics of two side-by-side plates in hypersonic rarefied-gas flows. J of Spacecraft and Rockets, 2002, 39: 910-916

20 Koppenwallner G, Legge H. Drag of bodies in rarefied hypersonic flow. In: Moss JN, Scott CD, eds. Progress in Astronautics and Aeronautics, Thermophysical Aspects of Reentry Flows. New York, AIAA, 1994. 44-59

21 Alam MM, Zhou Y. Flow around two side-by-side closely spaced circular cylinders. Journal of Fluids and Structures, 2007, 23: 799-805

22 Riabov VV. Numerical study of interference between simple-shape bodies in hypersonic flows. Computers and Structures, 2009, 87:651-663

23 张涵信, 沈孟育. 计算流体力学— 差分方法的原理和应用. 北京: 国防工业出版社, 2003 (Zhang Hanxin, Shen Mengyu. Computational Fluid Dynamics—Fundamentals and Applications of Finite Di erence Methods. Beijing: National Defence Industry Press,2003 (in Chinese))

24 Bird GA. The DS2V/3V program suite for DSMC calculations. In: Rarefied Gas Dynamics, 24th International Symposium, Melville, NY, 2005. 541-546

施引文献

资源附件(0)

访问统计