Multiple-relaxation-time lattice Boltzmann method for study of two-lid-driven cavity flow solution multiplicity

Abstract

As a fundamental subject in fluid mechanics, sophisticated cavity flow patterns due to the movement of multi-lids have been routinely analyzed by the computational fluid dynamics community. Unlike those reported computational studies that were conducted using more conventional numerical methods, this paper features employing the multiple-relaxation-time (MRT) lattice Boltzmann method (LBM) to numerically investigate the two-dimensional cavity flows generated by the movements of two adjacent lids. The obtained MRT-LBM results reveal a number of important bifurcation flow features, such as the symmetry and steadiness of cavity flows at low Reynolds numbers, the multiplicity of stable cavity flow patterns when the Reynolds number exceeds its first critical value, as well as the periodicity of the cavity flow after the second critical Reynolds number is reached. Detailed flow characteristics are reported that include the critical Reynolds numbers, the locations of the vortex centers, and the values of stream function at the vortex centers. Through systematic comparison against the simulation results obtained elsewhere by using the lattice Bhatnagar–Gross–Krook model and other numerical schemes, not only does the MRT-LBM approach exhibit fairly satisfactory accuracy, but also demonstrates its remarkable flexibility that renders the adjustment of its multiple relaxation factors fully manageable and, thus, particularly accommodates the need of effectively investigating the multiplicity of flow patterns with complex behaviors.