Simulation of Incompressible Flows in Two-Sided Lid-Driven Square Cavities. Part I - FDM

Abstract

The present paper computes the flow in a two-sided lid-driven square cavity by the Lattice Boltzmann Method (LBM). For some aspect ratios there exists a multiplicity of steady solutions, but the square cavity problem gives only a single steady solution for both the parallel and antiparallel motion of the walls. It is found that for parallel motion of the walls, there appears a pair of counter-rotating secondary vortices of equal size near the centre 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. Such a study is attempted in this paper through the LBM, as the results of the problem have the potential of being used for testing various solution methods for incompressible viscous flows. The results for the antiparallel motion of the walls are also presented in some detail. To lend credibility to the LBM results they are further compared with those obtained from a finite difference method (FDM).