Gas kinetic scheme in hypersonic flow simulation

XU Kun; CHEN Songze

doi:10.7527/S1000-6893.2014.0232

ACTA AERONAUTICAET ASTRONAUTICA SINICA >

2015 , Vol. 36 >Issue 1: 135 - 146

DOI: https://doi.org/10.7527/S1000-6893.2014.0232

Experiments and Numerical Simulations

Gas kinetic scheme in hypersonic flow simulation

XU Kun ,
CHEN Songze

Expand

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

Received date: 2014-07-25

Revised date: 2014-09-22

Online 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

Fold

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

Cite this article

XU Kun , CHEN Songze . Gas kinetic scheme in hypersonic flow simulation[J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2015 , 36(1) : 135 -146 . DOI: 10.7527/S1000-6893.2014.0232

References

[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.

Options

Outlines

模态框（Modal）标题

Abstract

Cite this article

References