Boltzmann-Rykov模型的有限体积方法计算

吴俊林; 李志辉; 彭傲平; 蒋新宇

doi:10.3879/j.issn.1000-0887.2014.02.002

Boltzmann-Rykov模型的有限体积方法计算

doi: 10.3879/j.issn.1000-0887.2014.02.002

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

基金项目: 国家自然科学基金(91016027);国家重点基础研究发展计划（973计划）（2014CB744100）

详细信息

作者简介:
吴俊林（1985—），男，四川会理人，硕士(Tel: +86-816-2465261; E-mail: wujunlin130@aliyun.com);

中图分类号: O356;V211.25
计量
- 文章访问数: 1446
- HTML全文浏览量: 126
- PDF下载量: 1137
- 被引次数: 0
出版历程
- 收稿日期: 2013-07-01
- 修回日期: 2013-12-09
- 刊出日期: 2014-02-15

Calculation of Boltzmann-Rykov Model Equation by Finite Volume Method

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

Funds: The National Natural Science Foundation of China(91016027); The National Basic Research Program of China (973 Program)（2014CB744100）

摘要

摘要: 构建一种三阶精度的有限体积格式，数值求解考虑转动非平衡影响的Boltzmann-Rykov模型方程.针对模型方程的速度空间离散得到各个离散速度坐标点上彼此独立的控制方程组，运用高阶精度的半离散化有限体积格式在位置空间对离散控制方程进行数值求解，时间项采用三阶Runge-Kutta方法推进，方程右端二体碰撞项采用中心近似技术.该有限体积格式在气体分子对流运动项上具有三阶精度，同时保证了分布函数的正定性和流通量守恒.计算结果与有限差分方法数值模拟结果和连续流区非定常激波管问题的Riemann精确解均吻合较好，说明基于有限体积法的Boltzmann-Rykov模型方程数值求解过程是正确的.
- Rykov模型方程 /
- 统一算法 /
- 有限体积方法
Abstract: A three order precision finite volume scheme was formulated to numerically solve the Boltzmann-Rykov model equation in which rotational energy was considered. This model equation was discretized into a series of equations at each discrete velocity point, and then a high order half-discretization finite volume scheme was used to compute these equations. Three order Runge-Kutta method was introduced for time marching, and central value in each cell was taken to approximate the average collision term. This finite volume scheme was of three order precision in convection term, while positive definiteness of the distribution functions and flux conservation were ensured. Results were compared with those of finite difference method and Riemann exact solution in continuum regime. The good coincidence shows validity of the solving process for the model equation by finite volume method.
- Rykov model equation /
- gas kinetic unified algorithm /
- finite volume method

HTML全文

参考文献(16)

[1]	Bird G A. Approach to translational equilibrium in a rigid sphere gas[J]. Phys Fluids,1963,6: 1518-1519.
[2]	Filbet F, Russo G. High order numerical methods for the space non-homogeneous Boltzmann equation[J]. Journal of Computational Physics,2003,186(2): 457-480.
[3]	李志辉, 吴振宇. 阿波罗指令舱稀薄气体动力学特征的蒙特卡罗数值模拟[J]. 空气动力学学报, 1996,14(2): 230-233.(LI Zhi-hui, WU Zhen-yu. Monte-Carlo numerical simulation of rarefied aerodynamic characters for Apollo spacecraft[J]. Acta Aerodynamica Sinica,1996,14(2): 230-233.（in Chinese）)
[4]	Mieussens L. Discrete velocity model and implicit scheme for the BGK equation of rarefied gas dynamics[J]. Mathematical Models and Methods in Applied Sciences,2000,10(8): 1121-1150.
[5]	Bird G A. Molecular Gas Dynamics [M]. Oxford: Clarendon Press, 1976.
[6]	沈青. DSMC方法与稀薄气流计算的发展[J]. 力学进展, 1996,26(1): 1-13.（SHEN Qing. DSMC method and the calculation of rarefied gas flow[J]. Advances in Mechanics,1996,26(1): 1-13.（in Chinese））
[7]	Bobylev A V, Cergignani C. Exact eternal solutions of the Boltzmann equation[J]. Journal of Statistical Physics,2002,106(5/6): 1019-1038.
[8]	Kolobov V I, Bayyuk S A. Construction of a unified continuum/kinetic solver for aerodynamic problems[J]. Journal of Spacecraft and Rockets,2005,42(4): 598-606.
[9]	Cheremisin F G, Agarwal R K. Computation of hypersonic shock structure in diatomic gases with rotational and vibrational relaxation using the generalized Boltzmann equation[C]// 46th AIAA Aerospace Sciences Meeting and Exhibit,2008. doi: 10.2514/6.2008-1269.
[10]	LI Zhi-hui, ZHANG Han-xin. Study on gas kinetic unified algorithm for flows from rarefied transition to continuum[J]. Journal of Computational Physics,2004,193(2): 708-738.
[11]	LI Zhi-hui, ZHANG Han-xin. Numerical investigation from rarefied flow to continuum by solving the Boltzmann model equation[J]. International Journal for Numerical Methods in Fluids,2003,42(4): 361-382.
[12]	ZHENG Ying-song, Struchtrup H. Ellipsoidal statistical Bhatnagar-Gross-Krook model with velocity-dependent collision frequency[J]. Physics of Fluids,2005,17(12): 103-127.
[13]	李志辉, 张涵信. 稀薄流到连续流的气体运动论统一数值算法初步研究[J]. 空气动力学学报, 2000,18(3): 255-263.（LI Zhi-hui, ZHANG Han-xin. Study on gas kinetic algorithm for flows from rarefied transition to continuum[J]. Acta Aerodynamica Sinica,2000,18(3): 255-263.（in Chinese））
[14]	Rykov V A. Model kinetic equation of a gas with rotational degrees of freedom[J]. Fluid Dynamics,1975,10(6): 959-966.
[15]	Rykov V A, Titarev V A, Shakhov E M. Shockwave structure in a diatomic gas based on a kinetic model[J]. Fluid Dynamics,2008,43(2): 316-326.
[16]	张涵信, 沈孟育. 计算流体力学——差分方法的原理和应用[M]. 北京: 国防工业出版社, 2003.(ZHANG Han-xin, SHEN Meng-yu. Computational Fluid Dynamics: Principles of Differential Methods and Applications [M]. Beijing: National Defence Industry Press, 2003.(in Chinese))