TY - JOUR
T1 - Transition Flow with an Incompressible Lattice Boltzmann Method
AU - Murdock , J. R.
AU - Ickes , J. C.
AU - Yang , S. L.
JO - Advances in Applied Mathematics and Mechanics
VL - 5
SP - 1271
EP - 1288
PY - 2018
DA - 2018/05
SN - 9
DO - http://doi.org/10.4208/aamm.OA-2016-0103
UR - https://global-sci.org/intro/article_detail/aamm/12200.html
KW - Multiple relaxation time, lattice Boltzmann, transition, high Reynolds number flow, incompressible flow, lid driven cavity.
AB - <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>