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Transition Flow with an Incompressible Lattice Boltzmann Method

Part of: Optics, electromagnetic theory - General

Published online by Cambridge University Press:  11 July 2017

J. R. Murdock ,
J. C. Ickes  and
S. L. Yang
J. R. Murdock*
Affiliation:
Department of Mechanical Engineering-Engineering Mechanics, Michigan Technological University, 1400 Townsend Drive, Houghton, MI 49931, USA
J. C. Ickes*
Affiliation:
Department of Mechanical Engineering-Engineering Mechanics, Michigan Technological University, 1400 Townsend Drive, Houghton, MI 49931, USA
S. L. Yang*
Affiliation:
Department of Mechanical Engineering-Engineering Mechanics, Michigan Technological University, 1400 Townsend Drive, Houghton, MI 49931, USA
*
*Corresponding author. Email:jrmurdoc@mtu.edu (J. R. Murdock), ickesjc@gmail.com (J. C. Ickes), slyang@mtu.edu (S. L. Yang)
*Corresponding author. Email:jrmurdoc@mtu.edu (J. R. Murdock), ickesjc@gmail.com (J. C. Ickes), slyang@mtu.edu (S. L. Yang)
*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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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.

Keywords

Multiple relaxation timelattice Boltzmanntransitionhigh Reynolds number flowincompressible flowlid driven cavity

MSC classification

Secondary: 78A48: Composite media; random media
Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 9 , Issue 5 , October 2017 , pp. 1271 - 1288
Copyright
Copyright © Global-Science Press 2017 

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