Multiplicity of steady solutions in lid-driven cavity flows using an Incompressible Generalized Lattice Boltzmann Method

چکیده مقاله

Abstract This work is concerned with the computation of two-sided lid-driven square cavity flows by the Lattice Boltzmann Method (LBM) to obtain multiple stable solutions. The velocity field is solved by an incompressible generalized lattice Boltzmann method. In the two-sided square cavity two of the walls move with equal velocity move in such a way that parallel walls move in opposite directions with the same 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. At low Reynolds numbers, the resulting flow field is symmetric with respect to one of the cavity diagonals for the two-sided driven cavity, while it is symmetric with respect to both cavity diagonals for the four-sided driven cavity. It is found that for parallel motion of the walls, there appears a pair of counter-rotating secondary vortices of equal size near the center of a wall. Because of symmetry, this pair of counter-rotating vortices has similar shapes and their detailed study as to how they grow with increasing Reynolds number has not yet been made by lattice Boltzmann Method.