@Article{AAMM-9-1271,
author = {Murdock , J. R.Ickes , J. C. and Yang , S. L.},
title = {Transition Flow with an Incompressible Lattice Boltzmann Method},
journal = {Advances in Applied Mathematics and Mechanics},
year = {2018},
volume = {9},
number = {5},
pages = {1271--1288},
abstract = {<p style="text-align: justify;">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.</p>},
issn = {2075-1354},
doi = {https://doi.org/10.4208/aamm.OA-2016-0103},
url = {http://global-sci.org/intro/article_detail/aamm/12200.html}
}