Boltzmann–BGK approach to simulating weakly compressible 3D turbulence: comparison between lattice Boltzmann and gas kinetic methods

References

• Bhatnagar , P. L. , Gross , E. P. and Krook , M. 1954 . A model for collision processes in gases I. Small amplitude processes in charged and neutral one-component systems . Physical Review , 94 : 511 – 525 .
   Web of Science ®Google Scholar
• Leemput , P. V. , Vanroose , W. and Roose , D. 2006 . Numerical analysis of the constrained runs initialization scheme for a lattice Boltzman model . The Third International Conference for Messoscopic Methods in Engineering and Science , ICMEES, 24–28 July 2006, Virginia, USA.
   Google Scholar
• He , X. and Luo , L.-S. 1997 . Theory of the lattice Boltzmann equation: from Boltzmann equation to lattice Boltzmann equation . Physical Review E , 56 : 6811 – 6817 .
   Web of Science ®Google Scholar
• Chen , S. , Wang , Z. , Shan , X. and Doolen , G. D. 1992 . Lattice Boltzmann computational fluid dynamics in three dimensions . Journal of Statistical Physics , 68 : 397 – 400 .
   Web of Science ®Google Scholar
• Benzi , R. , Struglia , M. V. and Tripiccione , R. 1996 . Extended self-similarity in numerical simulations of three-dimensional anisotropic turbulence . Physical Review E , 53 : R5565 – R5568 .
   PubMed Web of Science ®Google Scholar
• Luo , L.-S. , Qi , D. and Wang , L.-P. 2002 . Applications of the lattice Boltzmann method to complex and turbulent flows in . Lecture Notes in Computational Science and Engineering , 21 : 123 – 130 . edited by Breuer, M., Durst, F., and Zenger, C.
   Google Scholar
• Yu , H. , Girimaji , S. S. and Luo , L.-S. 2005 . Lattice Boltzmann simulations of decaying homogeneous isotropic turbulence . Physical Review E , 71 : 016708
   Web of Science ®Google Scholar
• Yu , H. , Girimaji , S. S. and Luo , L.-S. 2005 . DNS and LES of decaying isotropic turbulence with and without frame rotation using lattice Boltzmann method . Journal of Computational Physics , 209 : 599 – 616 .
   Web of Science ®Google Scholar
• Yu , D. and Girimaji , S. S. 2005 . DNS of homogeneous shear turbulence revisited with the lattice Boltzmann method . Journal of Turbulence , 6 : 1 – 17 .
   Web of Science ®Google Scholar
• Lee , K. , Yu , D. and Girimaji , S. S. 2006 . Lattice Boltzmann DNS of decaying compressible isotropic turbulence with temperature fluctuations . International Journal of Computational Fluid Dynamics , 20 : 401 – 413 .
   Web of Science ®Google Scholar
• Sakurai , A. and Takayama , F. 2003 . Molecular kinetic approach to the problem of compressible turbulence . Physics of Fluids , 15 : 1282 – 1293 .
   Web of Science ®Google Scholar
• Xu , K. 2001 . A Gas-kinetic BGK scheme for the Navier–Stoke equation and its connection with artificial dissipation and godunov method . Journal of Computational Physics , 171 : 289 – 335 .
   Web of Science ®Google Scholar
• Xu , K. and He , X. 2003 . Lattice Boltzmann method and gas-kinetic BGK scheme in the low-mach number viscous flow simulations . Journal of Computational Physics , 190 : 100 – 117 .
   Web of Science ®Google Scholar
• Su , M. , Xu , K. and Ghidaoui , M. S. 1999 . Low-speed flow simulation by the gas-kinetic scheme . Journal of Computational Physics , 150 : 17 – 39 .
   Web of Science ®Google Scholar
• Xu , K. , Mao , M. and Tang , L. 2005 . A multidimensional gas-kinetic BGK scheme for hypersonic viscous flow . Journal of Computational Physics , 203 : 405 – 421 .
   Web of Science ®Google Scholar
• Li , Q. , Fu , S. and Xu , K. 2005 . Applications of gas-kinetic scheme with kinetic boundary conditions in hypersonic flow . AIAA Journal , 43 : 2170 – 2176 .
   Web of Science ®Google Scholar
• May , G. , Srinivasan , B. and Jameson , A. 2007 . An improved gas-kinetic BGK finite volume method for three-dimensional transonic flow . Journal of Computational Physics , 220 : 856 – 878 .
   Web of Science ®Google Scholar
• May , G. , Srinivasan , B. and Jameson , A. 2005 . Calculating three-dimensional transonic flow using a gas-kinetic BGK finite-volume method . AIAA Journal , : 2005 – 1397 .
   Google Scholar
• Mansour , N. N. and Wray , A. A. 1994 . Decay of isotropic turbulence at low Reynolds number . Physics of Fluids , 6 : 808 – 814 .
   Web of Science ®Google Scholar
• Huang , M.-J. and Leonard , A. 1994 . Power-law decay of homogeneous turbulence at low Reynolds numbers . Physics of Fluids , 6 : 3765 – 3775 .
   Web of Science ®Google Scholar
• Samtaney , R. , Pullin , D. I. and Kosovic , B. 2001 . Direct numerical simulation of decaying compressible turbulence . Physics of Fluids , 13 : 1415 – 1430 .
   Web of Science ®Google Scholar
• Anderson , J. D. J. R. 1995 . Computational Fluid Dynamics: the Basics with Applications , New York : McGraw-Hill .
   Google Scholar
• Lallemand , P. and Luo , L.-S. 2003 . Theory of the Lattice Boltzmann method: acoustic and thermal properties in two and three dimensions . Physical Review E , 68 : 036706
   Web of Science ®Google Scholar
• Chae , D. , Kim , C. and Rho , O. 2000 . Development of an improved gas-kinetic BGK scheme for inviscid and viscous flows . Journal of Computational Physics , 158 : 1 – 27 .
   Web of Science ®Google Scholar
• Pope , S. B. 2000 . Turbulent Flows , 160 Cambridge , , England : Cambridge University Press .
   Google Scholar