高阶气体动理学格式在湍流数值模拟中的应用

曹贵瑜; 潘亮; 徐昆

doi:10.7638/kqdlxxb-2020.0156

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高阶气体动理学格式在湍流数值模拟中的应用

专栏——计算流体力学高精度格式及其应用 | 更新时间：2026-05-28

- 高阶气体动理学格式在湍流数值模拟中的应用
- High-order gas-kinetic scheme for numerical simulation of turbulence
- 空气动力学学报 2021年39卷第1期页码：168-176
- 作者机构：
  
  1. 南方科技大学前沿与交叉科学研究院,深圳,518055
  2. 北京师范大学数学科学学院, 数学与复杂系统教育部重点实验室,北京,100875
  3. 香港科技大学数学系,香港
- 作者简介：
  
  曹贵瑜(1994-), 男, 河南信阳人, 博士, 研究方向: 气体动理学格式, 湍流模拟和建模.E-mail: caogy@sustech.edu.cn
  徐昆(1966-), 教授, 研究方向: 计算流体力学高精度格式, 稀薄气体动理学, 输运问题的多尺度建模等.E-mail: makxu@ust.hk
- 基金信息：
  
  国家自然科学基金（91852114，11772281，11701038）;国家数值风洞工程（ NNW）
- DOI：10.7638/kqdlxxb-2020.0156
  中图分类号： O357.5
- 纸质出版：2021
- 稿件说明：
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曹贵瑜, 潘亮, 徐昆. 高阶气体动理学格式在湍流数值模拟中的应用[J]. 空气动力学学报, 2021, 39(1): 168-176.

CAO Guiyu, PAN Liang, XU Kun. High-order gas-kinetic scheme for numerical simulation of turbulence[J]. 2021, 39(1): 168-176.
曹贵瑜, 潘亮, 徐昆. 高阶气体动理学格式在湍流数值模拟中的应用[J]. 空气动力学学报, 2021, 39(1): 168-176. DOI： 10.7638/kqdlxxb-2020.0156.

CAO Guiyu, PAN Liang, XU Kun. High-order gas-kinetic scheme for numerical simulation of turbulence[J]. 2021, 39(1): 168-176. DOI： 10.7638/kqdlxxb-2020.0156.

摘要

本文回顾了高阶气体动理学格式在湍流数值模拟中的应用。与传统的Riemann求解器相比，气体动理学格式可以提供时空耦合的演化过程，这对发展高精度格式十分重要。因此，基于两步四阶时间离散和高精度WENO重构，发展了具有四阶时间精度的气体动理学格式。该格式有更高的数值精度和稳定性，并且具有更好的处理复杂流动问题的能力。目前，两步四阶格式已经成功地应用到低雷诺数湍流直接数值模拟和高雷诺数工程湍流RANS模拟中，包括低速槽道湍流、超声速均匀各向同性衰减湍流、二维亚声速翼型湍流和三维跨声速翼身湍流等。数值结果表明该格式对湍流直接数值模拟和湍流RANS模拟具有高数值精度和高数值稳定性。下一步将利用高阶气体动理学格式研究更具有挑战性的可压缩湍流问题，例如超声速湍流边界层和激波边界相互作用等。

Abstract

We review the application of high-order gas-kinetic scheme (HGKS) in the numerical simulations of turbulence. HGKS was developed based on the two-stage fourth-order temporal discretization and high-order weighted essentially non-oscillation (WENO) reconstruction. Compared with the classical Riemann solvers

the high-order temporal evolution process

which is extremely helpful in the design of robust

accurate

and efficient higher-order schemes

can be used to construct a spatial-temporal coupled gas-kinetic flux solver. Currently

HGKS has been successfully applied in the direct numerical simulations and Reynolds averaged Navier-Stokes (RANS) simulations of turbulence

including low-speed turbulent channel flows

the decaying supersonic isotropic turbulence

the subsonic NACA0012 airfoil turbulence

and the transonic ARA M100 wing-body turbulence. The numerical results show that HGKS has the high accuracy and outstanding robustness for turbulence simulations. In summary

the HGKS provides a powerful computational tool for studying turbulent flows

especially for compressible turbulence. In the future

more challenging studies will be conducted

including the supersonic turbulent boundary layers and the shock-boundary layer interaction.

关键词

Keywords

references

POPE S B. Turbulentflows[M]. Cambridge, 2001.

KIM J, MOIN P, MOSER R. Turbulence statistics in fully developedchannel flow at low Reynolds number[J]. J Fluid Mech, 1987, 177: 133-166.

MOIN P, MAHESH K. Direct numerical simulation: A tool in turbulence research[J]. Annu Rev Fluid Mech, 1998, 30: 539-578.

LEE M, MOSER R. Direct numerical simulation of turbulent channel flow up to Re τ ≈5200[J ] . J Fluid Mech, 2017, 774: 395-415.

WANG L P, CHEN S Y, BRASSEUR J G, et al. Examination of hypotheses in the Kolmogorov refined turbulence theory through high-resolution simulations. Part 1. Velocity field[J]. J Fluid Mech, 1996, 309: 113-156.

CHEN S Y, DOOLEN G D. Lattice Boltzmann method for fluid flows[J]. Annu Rev Fluid Mech, 1998, 30: 329-364.

LELE S K. Compact finite difference schemes with spectral-like resolution[J]. J Comput Phys, 1992, 103: 16-42.

GAO H, FU D X, MA Y W, et al. Direct numerical simulation of supersonic turbulent boundary layer flow[J]. Chinese Physics Letters, 2005, 22(7): 1709.

WANG J C, WANG L P, XIAO Z L, et al. A hybrid numerical simulation of isotropic compressible turbulence[J]. J Comput Phys, 2010, 229: 5257-5279.

SLOTNICK J, KHODADOUST A, ALONSO J, et al. CFD vision 2030 study: A path to revolutionary computational aerosciences[R]. NASA/CR-2014-218178.

XU K. A gas-kinetic BGK scheme for the Navier-Stokes equations and its connection with artificial dissipation and Godunov method[J]. J Comput Phys, 2001, 171: 289-335.

XU K. Direct modeling for computational fluid dynamics: Construction and application of unified gas kinetic schemes[M]. World Scientific, 2015.

BHATNAGAR P L, GROSS E P, KROOK M. A model for collision processes in gases. I. Small amplitude processes in charged and neutral one-component systems[J]. Physical Review, 1954, 94(3): 511.

JIANG G S, SHU C W. Efficient implementation of weighted ENO schemes[J]. J Comput Phys, 1996, 126: 202-228.

CASTRO M, COSTA B, DON W S. High order weighted essentially non-oscillatory WENO-Z schemes for hyperbolic conservation laws[J]. J Comput Phys, 2011, 230: 1766-1792.

LI Q, XU K, FU S. A high-order gas-kinetic Navier-Stokes flow solver[J]. Journal of Computational Physics, 2010, 229: 6715-6731.

LUO J, XU K. A high-order multidimensional gas-kinetic scheme for hydrodynamic equations[J]. Science China Technological Sciences, 2013, 56: 2370-2384.

LI J Q, DU Z F. A two-stage fourth order time-accurate discretization for Lax-Wendroff type flow solvers I. Hyperbolic conservation laws[J]. SIAM J Sci Computing, 2016, 38: 3046-3069.

PAN L, XU K, LI Q B, et al. An efficient and accurate two-stage fourth-order gas-kinetic scheme for the Navier-Stokes equations[J]. J Comput Phys, 2016, 326: 197-221.

JI X, ZHAO F, SHY Y W, et al. A family of high-order gas-kinetic schemes and its comparison with Riemann solver based high-order methods[J]. Journal of Computational Physics, 2018, 356: 150-173.

ZHAO F, JI X, SHY Y W, et al. Compact higher-order gas-kinetic schemes with spectral-like resolution for compressible flow simulations[J]. Advances in Aerodynamics, 2019, 1: 13.

FU S, LI Q. Numerical simulationof compressible mixing layers[J]. International Journal of Heat and Fluid Flow, 2006, 27: 895-901.

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.

CHEN H, KANDASAMY S, ORSZAG S, et al. Extended Boltzmann kinetic equation for turbulent flows[J]. Science, 2003, 301: 633-636.

JIANG J, QIAN Y. Implicit gas-kinetic BGK scheme with multigrid for 3D stationary transonic high-Reynolds number flows[J]. Computers Fluids, 2012, 66: 21-28.

PAN D, ZHONG C, LI J, et al. A gas-kinetic scheme for the simulation of turbulent flows on unstructured meshes[J]. International Journal for Numerical Methods in Fluids, 2016, 82: 748-769.

RIGHI M. A gas-kinetic scheme for turbulent flow[J]. Flow, Turbulence and Combustion, 2016, 97: 121-139.

LI J, ZHONG C, PAN D, et al. A gas-kinetic scheme coupled with SST model for turbulent flows[J]. Computers Mathematics with Applications, 2016.

TAN S, LI Q, XIAO Z, et al. Gas kinetic scheme for turbulence simulation[J]. Aerospace Science and Technology, 2018, 78: 214-227.

CAO G, SU H, XU J, et al. Implicit high-order gas kinetic scheme for turbulence simulation[J]. Aerospace Science and Technology, 2019, 92: 958-971.

TITAREV V A, TORO E F. Finite volume WENO schemes for three-dimensional conservation laws[J]. J Comput Phys, 2014, 201: 238-260.

WOODWARD P, COLELLA P. Numerical simulations of two-dimensional fluid flow with strong shocks[J]. J Comput Phys, 1984, 54: 115-173.

BO Y T, WANG P, GUO Z L, et al. DUGKS simulations of three-dimensional Taylor-Green vortex flow and turbulent channel flow[J]. Computers Fluids, 2017, 1559-21.

CAO G. High-order gas-kinetic schemes for turbulence modeling and simulation[D]. Hong Kong: Hong Kong University of Science and Technology, 2020.

CAO G, PAN L, XU K. Three dimensional high-order gas-kinetic scheme for supersonic isotropic turbulence I: Criterion for direct numerical simulation[J]. Computers Fluids, 2019, 192: 104273.

SAMTANEY R, PULLIN D I, KOSOVIC B. Direct numerical simulation of decaying compressible turbulence and shocklet statistics[J]. Physics of Fluids, 2001, 13(5): 1415-1430.

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