高超声速计算中的气体动理学格式

doi:10.7527/S1000-6893.2014.0232

实验与数值模拟

本期目录 | 过刊浏览 | 高级检索

前一篇 | 后一篇

高超声速计算中的气体动理学格式

徐昆, 陈松泽

香港科技大学数学系, 香港

收稿日期:2014-07-25 修回日期:2014-09-22 出版日期:2015-01-15 发布日期:2014-09-23
通讯作者: 徐昆,Tel.: 00852-23587433 E-mail: makxu@ust.hk E-mail:makxu@ust.hk
作者简介:徐昆男, 博士, 教授。主要研究方向:计算流体力学、数值方法、高阶格式、气体动理学格式和统一气体动理学格式等。 Tel: 00852-23587433 E-mail: makxu@ust.hk;陈松泽男, 博士研究生。主要研究方向:计算流体力学、稀薄气体、气体动理学格式等。 Tel: 00852-59430791 E-mail: jacksongze@pku.edu.cn
基金资助:
香港研资局基金(621011, 620813); 高温气体动力学国家重点实验室开放基金(2013KF03); 北京大学湍流与复杂系统国家重点实验室资助

Gas kinetic scheme in hypersonic flow simulation

XU Kun, CHEN Songze

Department of Mathematics, The Hong Kong University of Science and Technology, Hong Kong, China

Received:2014-07-25 Revised:2014-09-22 Online:2015-01-15 Published:2014-09-23
Supported by:
Hong Kong Research Grant Council (621011, 620813); State Key Laboratory of High-temperature Gas Dynamics Open Fund (2013KF03); Supported by State Key Laboratory for Turbulence and Complex Systems of Peking University

摘要/Abstract

摘要：

回顾了高超声速连续流部分的计算流体力学(CFD)方法,总结了近些年兴起的气体动理学格式。阐述了该格式的构造机制,强调了将物理规律直接用于构造数值方法的思路。结合一些应用实例,例如激波相互作用、激波边界层相互作用以及边界层分离等高超声速问题,说明了这种构造思路给数值模拟带来的优点。从高超声速的发展历程来看,气体动理学格式的构造过程包含了更基础的物理规律,而且具有多尺度的特性。这些特性有助于研究复杂的高超声速问题。介观或者微观角度直接构造数值方法的发展趋势为高超声速计算工具指出了可能的发展方向。

关键词: 高超声速, 气体动理学格式, 滑移边界条件, 激波相互作用, 激波边界层干扰

Abstract:

For hypersonic flow simulation, a review of computation fluid dynamics (CFD) and a summary of gas kinetic scheme are presented in this paper. The mechanism underlying the construction of gas kinetic scheme is clarified by comparing it with the traditional CFD method. The importance of direct modeling and the implementation of the physical laws in a discretized space are emphasized. Through some classical hypersonic applications in recent years, such as the shock/shock interaction, shock wave/boundary layer interaction, and hypersonic boundary layer separation problems, the advantages of the methodology are also demonstrated. As a trend of CFD, the gas kinetic scheme includes more fundamental physical laws in its algorithm construction, and the multiple scale nature makes the kinetic scheme feasible for the hypersonic applications. The principle of direct modeling and the methodology of constructing numerical schemes from mesoscopic or microscopic flow dynamics would benefit the development of reliable flow solvers, especially for the high speed flow.

Key words: hypersonic, gas kinetic scheme, slip boundary condition, shock/shock interaction, shock wave/boundary layer interaction

中图分类号:

徐昆, 陈松泽. 高超声速计算中的气体动理学格式[J]. 航空学报, 2015, 36(1): 135-146.

XU Kun, CHEN Songze. Gas kinetic scheme in hypersonic flow simulation[J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2015, 36(1): 135-146.

参考文献

[1] Tsien H S. Similarity laws of hypersonic flows[J]. Journal of Mathematical Physics, 1946, 25(3): 247-251.
[2] Bertin J J, Cummings R M. Critical hypersonic aerothermodynamic phenomena[J]. Annual Review of Fluid Mechanics, 2006, 38: 129-157.
[3] Anderson Jr J D. Hypersonic and high-temperature gas dynamics[M]. 2nd. Virginia: AIAA, 2006: 200.
[4] Rasmussen M. Hypersonic flow[M]. New York: John Wiley & Sons, Inc., 1994: 322.
[5] Bushnell D M. Hypersonic flight experimentation-status and shortfalls[C]//Future Aerospace Technology in the Service of the Alliance. Hampton,VA: NASA Langley Research Center, 1997.
[6] Moretti G, Abbett M. A time-dependent computational method for blunt-body flows[J]. AIAA Journal, 1966, 4(12): 2136-2141.
[7] Shang J S. Three decades of accomplishments in computational fluid dynamics[J]. Progress in Aerospace Sciences, 2004, 40(3): 173-197.
[8] MacCormack R. The effect of viscosity in hypervelocity impact cratering[J]. Journal of Spacecraft and Rockets, 2003, 40(5): 757-763.
[9] Shang J S, Hankey Jr W L. Numerical solution of the compressible Navier-Stokes equations for a three-dimensional corner[C]//AIAA Aerospace Sciences Meeting. California: AIAA, 1977.
[10] Godunov S K. A difference method for numerical calculation of discontinuous solutions of the equations of hydrodynamics[J]. Matematicheskii Sbornik, 1959, 89(3): 271-306.
[11] Steger J L, Warming R F. Flux vector splitting of the inviscid gas dynamic equations with application to finite-difference methods[J]. Journal of Computational Physics, 1981, 40(2): 263-293.
[12] van Leer B. Flux-vector splitting for the Euler equations[C]//Eighth International Conference on Numerical Methods in Fluid Dynamics. Berlin: Springer Heidelberg, 1982: 507-512.
[13] Roe P L. Approximate Riemann solvers, parameter vectors, and difference schemes[J]. Journal of Computational Physics, 1981, 43(2): 357-372.
[14] Roe P L. Characteristic-based schemes for the Euler equations[J]. Annual Review of Fluid Mechanics, 1986, 18(1): 337-365.
[15] Einfeldt B. On Godunov-type methods for gas dynamics[J]. SIAM Journal on Numerical Analysis, 1988, 25(2): 294-318.
[16] Toro E F, Spruce M, Speares W. Restoration of the contact surface in the HLL-Riemann solver[J]. Shock Waves, 1994, 4(1): 25-34.
[17] Harten A. High resolution schemes for hyperbolic conservation laws[J]. Journal of Computational Physics, 1983, 49(3): 357-393.
[18] Zhang H X. Non-oscillatory and non-free-parameter dissipation difference scheme[J]. Acta Aerodynamica Sinica, 1988, 6(2): 143-165 (in Chinese). 张涵信. 无波动、无自由参数的耗散差分格式[J]. 空气动力学学报, 1988, 6(2): 143-165.
[19] Harten A, Engquist B, Osher S, et al. Uniformly high order accurate essentially non-oscillatory schemes, III[J]. Journal of Computational Physics, 1987, 131(2): 231-303.
[20] Liu X D, Osher S, Chan T. Weighted essentially non-oscillatory schemes[J]. Journal of Computational Physics, 1994, 115(1): 200-212.
[21] Lele S K. Compact finite difference schemes with spectral-like resolution[J]. Journal of Computational Physics, 1992, 103(1): 16-42.
[22] Zhong X L. Direct numerical simulation of hypersonic boundary-layer transition over blunt leading edges. I-A new numerical method and validation[C]//AIAA, Aerospace Sciences Meeting & Exhibit. Reno, NV,USA: AIAA, 1997.
[23] Zhong X L. Direct numerical simulation of hypersonic boundary-layer transition over blunt leading edges. II-Receptivity to sound[C]//AIAA, Aerospace Sciences Meeting & Exhibit. Reno, NV: AIAA, 1997.
[24] Zhong X. High-order finite-difference schemes for numerical simulation of hypersonic boundary-layer transition[J]. Journal of Computational Physics, 1998, 144(2): 662-709.
[25] Adams N A, Shariff K. A high-resolution hybrid compact-ENO scheme for shock-turbulence interaction problems[J]. Journal of Computational Physics, 1996, 127(1): 27-51.
[26] Wang J, Wang L P, Xiao Z, et al. A hybrid numerical simulation of isotropic compressible turbulence[J]. Journal of Computational Physics, 2010, 229(13): 5257-5279.
[27] Davis R T. Numerical solution of the hypersonic viscous shock-layer equations[J]. AIAA Journal, 1970, 8(5): 843-851.
[28] Rubin S G, Lin A. Marching with the parabolized Navier-Stokes equations[J]. Israel Journal of Technology, 1980, 18: 21-31.
[29] Rubin S G, Tannehill J C. Parabolized/reduced Navier-Stokes computational techniques[J]. Annual Review of Fluid Mechanics, 1992, 24(1): 117-144.
[30] Prendergast K H, Xu K. Numerical hydrodynamics from gas-kinetic theory[J]. Journal of Computational Physics, 1993, 109(1): 53-66.
[31] Xu K, Prendergast K H. Numerical Navier-Stokes solutions from gas kinetic theory[J]. Journal of Computational Physics, 1994, 114(1): 9-17.
[32] Xu K. A gas-kinetic BGK scheme for the Navier-Stokes equations and its connection with artificial dissipation and Godunov method[J]. Journal of Computational Physics, 2001, 171(1): 289-335.
[33] Harris S. An introduction to the theory of the Boltzmann equation[M]. New York: Dover Publications, Inc., 1994: 322.
[34] Ohwada T. On the construction of kinetic schemes[J]. Journal of Computational Physics, 2002, 177(1): 156-175.
[35] Ohwada T, Kobayashi S. Management of discontinuous reconstruction in kinetic schemes[J]. Journal of Computational Physics, 2004, 197(1): 116-138.
[36] Luo J, Xu K. A high-order multidimensional gas-kinetic scheme for hydrodynamic equations[J]. Science China Technological Sciences, 2013, 56(10): 2370-2384.
[37] Ohwada T, Adachi R, Xu K, et al. On the remedy against shock anomalies in kinetic schemes[J]. Journal of Computational Physics, 2013, 255: 106-129.
[38] Xu K, Huang J C. A unified gas-kinetic scheme for continuum and rarefied flows[J]. Journal of Computational Physics, 2010, 229(20): 7747-7764.
[39] Gnoffo P A. Updates to multi-dimensional flux recon-struction for hypersonic simulations on tetrahedral grids[C]//48th AIAA Aerospace Sciences Meeting. Orlando, FL: AIAA, 2010.
[40] Xu K, Mao M, Tang L. A multidimensional gas-kinetic BGK scheme for hypersonic viscous flow[J]. Journal of Computational Physics, 2005, 203(2): 405-421.
[41] Holden M S, Wadhams T P. A review of experimental studies for DSMC and Navier-Stokes code validation in laminar regions of shock/shock and shock boundary layer interaction including real gas effects in hyper-velocity flows[C]//36th AIAA Thermophysics Conference. Orlando, FL: AIAA, 2003.
[42] Candler G V, Nompelis I, Druguet M C. Navier-Stokes predictions of hypersonic double-cone and cylinder-flare flow fields[C]//AIAA Conference. Xi'an ,China: AIAA, 2001.
[43] Gaitonde D V, Canupp P W, Holden M S. Heat transfer predictions in a laminar hypersonic viscous/inviscid interaction[J]. Journal of Thermophysics and Heat Transfer, 2002, 16(4): 481-489.
[44] Knight D, Longo J, Drikakis D, et al. Assessment of CFD capability for prediction of hypersonic shock interactions[J]. Progress in Aerospace Sciences, 2012, 48: 8-26.
[45] Fukui S, Kaneko R. Analysis of ultra-thin gas film lubrication based on linearized Boltzmann equation: first report—derivation of a generalized lubrication equation including thermal creep flow[J]. Journal of Tribology, 1988, 110(2): 253-261.
[46] Li Q, Fu S, Xu K. Application of gas-kinetic scheme with kinetic boundary conditions in hypersonic flow[J]. AIAA Journal, 2005, 43(10): 2170-2176.
[47] Markelov G N, Kudryavtsev A N, Ivanov M S. Continuum and kinetic simulation of laminar separated flow at hypersonic speeds[J]. Journal of Spacecraft and Rockets, 2000, 37(4): 499-506.
[48] Chanetz B, Benay R, Bousquet J M, et al. Experimental and numerical study of the laminar separation in hypersonic flow[J]. Aerospace Science and Technology, 1998, 2(3): 205-218.
[49] Graur I A, Ivanov M S, Markelov G N, et al. Comparison of kinetic and continuum approaches for simulation of shock wave/boundary layer interaction[J]. Shock Waves, 2003, 12(4): 343-350.
[50] Li Q, Xu K, Fu S. A high-order gas-kinetic Navier-Stokes flow solver[J]. Journal of Computational Physics, 2010, 229(19): 6715-6731.
[51] Xuan L J, Xu K. A new gas-kinetic scheme based on analytical solutions of the BGK equation[J]. Journal of Computational Physics, 2013, 234: 524-539.
[52] Liu N. High-order accurate gas-kinetic schemes[D]. Beijing: Peking University, 2013 (in Chinese). 刘娜. 高精度气体动理学格式[D]. 北京: 北京大学, 2013.
[53] Righi M. A modified gas-kinetic scheme for turbulent flow[J]. Communications in Computational Physics 2014, 16(1): 239-263.
[54] Kumar G, Girimaji S S, Kerimo J. WENO-enhanced gas-kinetic scheme for direct simulations of compressible transition and turbulence[J]. Journal of Computational Physics, 2013, 234: 499-523.
[55] Sun W, Jiang S, Xu K. Asymptotic preserving unified gas kinetic scheme for grey radiative transfer equations[J]. Preprint, 2015.

E-mail：hkxb@buaa.edu.cn

关于我们

期刊社服务

专业学科

封面文章

友情链接

主管单位：中国科学技术协会主办单位：中国航空学会北京航空航天大学

高超声速计算中的气体动理学格式

Gas kinetic scheme in hypersonic flow simulation

PDF (PC)

可视化

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 15

编辑推荐

Metrics

本文评价

[1]	孙志坤, 史志伟, 张伟麟, 李铮, 孙琪杰. 等离子体激励器对高速翼型升阻特性的影响[J]. 航空学报, 2022, 43(S2): 23-39.
[2]	化为卓, 高岭, 陈戈, 李益文, 巩耕, 王延涛, 魏彪. 基于等离子体炬的磁流体动力学实验系统[J]. 航空学报, 2022, 43(S2): 1-7.
[3]	黄依峰, 曾舒华, 江中正, 陈伟芳. 非线性耦合本构在高空侧向喷流中的数值研究[J]. 航空学报, 2022, 43(S2): 8-22.
[4]	罗凯, 王永海, 汪球, 栗继伟, 李峥, 聂春生, 李铮. 高焓风洞中等离子体激励流动控制试验[J]. 航空学报, 2022, 43(S2): 89-96.
[5]	张旭东, 李铮, 董昊, 高思源, 纪祖赑, 黎凯昕, 白光辉. 高超声速流场等离子体逆向喷流减阻特性[J]. 航空学报, 2022, 43(S2): 115-123.
[6]	胡守超, 庄宇, 李贤, 江涛. 高超声速气动热标模HyHERM-Ⅰ试验[J]. 航空学报, 2022, 43(S2): 233-248.
[7]	李昊歌, 杨华, 杨雨欣, 陈伟芳. 高超声速升力体迎风面精细化降热优化设计[J]. 航空学报, 2022, 43(S2): 124-137.
[8]	吴东, 杨鸿, 赵文峰, 罗跃. 高超声速飞行器碳基结构高温应变测量[J]. 航空学报, 2022, 43(S2): 160-169.
[9]	聂春生, 袁野, 马伟, 曹占伟, 于明星. 主动引射气体参数对平板空气舵气动热影响[J]. 航空学报, 2022, 43(S2): 170-179.
[10]	马正雪, 罗振兵, 赵爱红, 周岩, 谢玮, 刘强, 朱寅鑫, 彭文强. 高超声速流场等离子体合成射流逆向喷流特性[J]. 航空学报, 2022, 43(S2): 192-203.
[11]	李珺, 王俊峰, 赵雅甜, 罗世彬. 面向非设计工况的激波针-喷流复合构型研究[J]. 航空学报, 2022, 43(9): 125949-125949.
[12]	刘传振, 孟旭飞, 刘荣健, 白鹏. 双后掠乘波体高超声速试验与数值分析[J]. 航空学报, 2022, 43(9): 126015-126015.
[13]	郑辉, 邱雷, 袁慎芳, 杨晓飞, 卢绪龙, 薛兆鹏. C/C热防护结构高温气流损伤导波监测实验方法[J]. 航空学报, 2022, 43(8): 225659-225659.
[14]	刘清扬, 雷娟棉, 刘周, 石磊, 周伟江. 适用于可压缩流动的γ-Re_θt-f_Re转捩模型[J]. 航空学报, 2022, 43(8): 125794-125794.
[15]	朱志斌, 尚庆, 沈清. 高超声速边界层转捩模型横流效应修正与应用[J]. 航空学报, 2022, 43(7): 125685-125685.