Numerical research on lid-driven cavity flows using a three-dimensional lattice Boltzmann model on non-uniform meshes

A lattice Boltzmann model combined with curvilinear coordinate is proposed for lid-driven cavity three-dimensional （3D） flows. For particle velocity distribution, the particle collision process is performed in physical domain, and the particle stream- ing process is carried out in the corresponding computational domain, which is transferred from the physical domain using in- terpolation method. For the interpolation calculation, a second-order upwind interpolation method is adopted on internal lattice nodes in flow fields while a second-order central interpolation algorithm is employed at neighbor-boundary lattice nodes. Then the above-mentioned model and algorithms are used to numerically simulate the 3D flows in the lid-driven cavity at Reynolds numbers of 100, 400 and 1000 on non-uniform meshes. Various vortices on the x-y, y-z and x-z symmetrical planes are suc- cessfully predicted, and their changes in position with the Reynolds number increasing are obtained. The velocity profiles of u component along the vertical centerline and w component along the horizontal centerline are both in good agreement with the data in literature and the calculated results on uniform meshes. Besides, the velocity vector distributions on various cross sec- tions in lid-driven cavity predicted on non-uniform meshes are compared with those simulated on uniform meshes and those in the literature. All the comparisons and validations show that the 3D lattice Boltzmann model and all the numerical algorithms on non-uniform meshes are accurate and reliable to predict effectively flow fields.