Multiplicity of steady solutions in two-dimensional lid-driven cavity flows by Lattice Boltzmann Method

This work is concerned with the computation of two- and four-sided lid-driven square cavity flows and also two-sided rectangular cavity flows with parallel wall motion by the Lattice Boltzmann Method (LBM) to obtain multiple stable solutions. In the two-sided square cavity two of the adjacent walls move with equal velocity and in the four-sided square cavity all the four walls move in such a way that parallel walls move in opposite directions with the same velocity; in the two-sided rectangular lid-driven cavity flow the longer facing walls move in the same direction with equal velocity. Conventional numerical solutions show that the symmetric solutions exist for all Reynolds numbers for all the geometries, whereas multiplicity of stable states exist only above certain critical Reynolds numbers. Here we demonstrate that Lattice Boltzmann method can be effectively used to capture multiple steady solutions for all the aforesaid geometries. The strategy employed to obtain these solutions is also described.