Year: 2017
Author: J. R. Murdock, J. C. Ickes, S. L. Yang
Advances in Applied Mathematics and Mechanics, Vol. 9 (2017), Iss. 5 : pp. 1271–1288
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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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aamm.OA-2016-0103
Advances in Applied Mathematics and Mechanics, Vol. 9 (2017), Iss. 5 : pp. 1271–1288
Published online: 2017-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 18
Keywords: Multiple relaxation time lattice Boltzmann transition high Reynolds number flow incompressible flow lid driven cavity.
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