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Transition Flow with an Incompressible Lattice Boltzmann Method

  • J. R. Murdock (a1), J. C. Ickes (a1) and S. L. Yang (a1)
Abstract
Abstract

Direct numerical simulations of the transition process from steady laminar to chaotic flow are considered in this study with the relatively new incompressible lattice Boltzmann equation. Numerically, a multiple relaxation time fully incompressible lattice Boltzmann equation is implemented in a 2D driven cavity. Spatial discretization is 2nd-order accurate, and the Kolmogorov length scale estimation based on Reynolds number (Re) dictates grid resolution. Initial simulations show the method to be accurate for steady laminar flows, while higher Re simulations reveal periodic flow behavior consistent with an initial Hopf bifurcation at Re 7,988. Non-repeating flow behavior is observed in the phase space trajectories above Re 13,063, and is evidence of the transition to a chaotic flow regime. Finally, flows at Reynolds numbers above the chaotic transition point are simulated and found with statistical properties in good agreement with literature.

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Corresponding author
*Corresponding author. Email: jrmurdoc@mtu.edu (J. R. Murdock), ickesjc@gmail.com (J. C. Ickes), slyang@mtu.edu (S. L. Yang)
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[1] P. L. Bhatnagar , E. P. Gross and M. Krook , A model for collision processes in gasses. I. Small amplitude processes in charged and neutral one-component systems, Phys. Rev., 94 (1954), pp. 511525.

[2] M. Bouzidi , D. D'Humieres , P. Lallemand and L. S. Luo , Lattice Boltzmann equation on a two-dimensional rectangular grid, J. Comput. Phys., 172 (2001), pp. 704717.

[3] C. H. Bruneau and M. Saad , The 2D lid-driven cavity problem revisited, Comput. Fluids, 35 (2006), pp. 326348.

[5] W. Cazemier , R. W. Verstappen and A. E. Veldman , Proper orthogonal decomposition and low-dimensional models for driven cavity flows, Phys. Fluids, 10 (1998), pp. 16851699.

[6] U. Ghia , K. N. Ghia and C. T. Shin , High-Re solutions for incompressible flow using the Navier-Stokes equations and a multigrid method, J. Comput. Phys., 48 (1982), pp. 387411.

[7] Z. Guo , B. Shi and N. Wang , Lattice BGK model for incompressible Navier-Stokes equation, J. Comput. Phys., 165 (2000), pp. 288306.

[8] X. He , G. D. Doolen and T. Clark , Comparison of the lattice Boltzmann method and the artificial compressibility method for Navier-Stokes equations, J. Comput. Phys., 179 (2002), pp. 439451.

[9] S. Hou , Q. Zou , S. Chen , G. Doolen and A. C. Cogley , Simulation of cavity flow by the lattice Boltzmann method, J. Comput. Phys., 118 (1995), pp. 329347.

[10] P. Lallemand and L. S. Luo , Theory of the lattice Boltzmann method: Dispersion, dissipation, isotropy, Galilean invariance, and stability, Phys. Rev. E, 61 (2000), 6546.

[11] P. Lammers , K. N. Beronov and R. Volkert et al., Lattice BGK direct numerical simulation of fully developed turbulence in incompressible plane channel flow, Comput. Fluids, 35 (2006), pp. 11371153.

[14] S. Marie , D. Ricot and P. Sagaut , Comparison between lattice Boltzmann method and Navier-Stokes high order schemes for computational aeroacoustics, J. Comput. Phys., 228 (2008), pp. 10561070.

[15] D. O. Martinez , W. H. Matthaeus , S. Chen and D. C. Montgomery , Comparison of spectral method and lattice Boltzmann simulations of two-dimensional hydrodynamics, Phys. Fluids, 6 (2006), pp. 12851298.

[16] G. R. McNamara and G. Zanetti , Use of the Boltzmann equation to simulate lattice-gas automata, Phys. Rev. Lett., 61 (1988), 2332.

[18] Y. F. Peng , Y. H. Shiau and R. R. Hwang , Transition in a 2-D lid driven cavity flow, Comput. Fluids, 32 (2003), pp. 337352.

[19] M. Poliashenko and C. K. Aidun , A direct method for computation of simple bifurcations, J. Comput. Phys., 121 (2006), pp. 246260.

[22] C. Zhang , Y. Cheng , S. Huang and J. Wu , Improving the stability of themultiple-relaxation-time lattice Boltzmann method by a viscosity counteracting approach, Adv. Appl. Math. Mech., 8 (2016), pp. 3751.

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Advances in Applied Mathematics and Mechanics
  • ISSN: 2070-0733
  • EISSN: 2075-1354
  • URL: /core/journals/advances-in-applied-mathematics-and-mechanics
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