  Wall-driven flow in square cavity has been studied extensively, yet it is
more frequently for the rectangular cavity flow occurring in practical
problems, and some flow characteristics about rectangular cavity have not been
fully investigated. As a promising numerical simulation tool, the Lattice
Boltzmann Method (LBM) is employed to simulate the lid-driven flow in a
two-dimensional rectangular cavity in this paper. First, the code is validated
for the standard square cavity, the velocity profiles, stream function values
and center positions of the primary and second vortexes at different Re are
presented and compared with previous researches. Then, the eddy dynamics of
rectangular cavities is simulated and discussed with Reynolds number (Re) in
the range of 4000-8000 and vertical to horizontal axis ratio (Ar) varied from
0.4 to 2.0, and the streamline and center migration of the primary vortex are
drawn realistically for rectangular cavity. In the end, the steady, periodic,
aperiodic and unstable phenomenon in the rectangular cavity is produced by LBM,
Re and Ar which play the significant role in the state transition of lid-driven
rectangular cavity flow are analyzed and summarized in detail. By the LBM
numerical simulation with 500x(500*Ar) grid, we have discovered that the flow
state in the rectangular cavity with a fixed Ar changes monotonically from
stable state, periodic state to aperiodic and unstable state with the increase
of Re, while the flow state in the rectangular cavity with a fixed Re varies
non-monotonically with the increase of Ar. Additionally, the cycle length of
periodic states varies with the change of Ar and Re.
