Transition Flow with an Incompressible Lattice Boltzmann Method (Advances in Applied Mathematics and Mechanics, 2018)
Direct numerical simulations of the transition process from steady laminarto chaotic flow are considered in this study with the relatively new incompressible latticeBoltzmann equation. Numerically, a multiple relaxation time fully incompressiblelattice Boltzmann equation is implemented in a 2D driven cavity. Spatial discretizationis 2nd-order accurate, and the Kolmogorov length scale estimation based on Reynoldsnumber ($Re$) dictates grid resolution. Initial simulations show the method to be accuratefor steady laminar flows, while higher $Re$ simulations reveal periodic flow behaviorconsistent with an initial Hopf bifurcation at $Re$ 7,988. Non-repeating flow behavioris observed in the phase space trajectories above $Re$ 13,063, and is evidence of the transitionto a chaotic flow regime. Finally, flows at Reynolds numbers above the chaotictransition point are simulated and found with statistical properties in good agreementwith literature.