Filter-matrix lattice Boltzmann simulation of lid-driven deep-cavity flows, Part I — Steady flows

This paper seeks to make a systematic study over a series of lid-driven flow in various deep cavities using the filter-matrix lattice Boltzmann (FMLB) model. A concise description of the FMLB model is presented in this paper, and important numerical considerations for effective use of the FMLB model are also clearly elucidated. In particular, the selection of a free parameter employed to appropriately control the weight of the third-order terms in the FMLB solution vector is carefully examined, resulting in some general suggestions that may render the FMLB stability consistently secured for simulations of different cavity flow scenarios. Employing the FMLB and the lattice Bhatnagar–Gross–Krook (LBGK) methods for comparison purpose, the first series of test cases correspond to the lid-driven cavity flows with a low Reynolds number (Re=0.01) at a variety of aspect ratios; the simulation results demonstrate that the FMLB model is superior to the LBGK method in terms of numerical stability and, particularly, the FMLB result can reach quite good agreement with the benchmark solution even if the aspect ratio goes up to 15. Then, the FMLB model is used to compute the steady flows for deep cavities with aspect ratios ranging from 1.5 to 7 and elevated Reynolds numbers ranging from 100 to 5000; a number of features of steady flows, such as the locations, strengths, and sizes of the vortices, as well as the effects of Reynolds number and aspect ratio on the vortex structure, are all predicted by the FMLB model with an obviously improved accuracy when compared to some other available numerical results.