A Generalized Lattice Boltzmann Method for Three-Dimensional Incompressible Fluid Flow Simulation

Abstract

In this work, a 19-bit Incompressible Generalized Lattice Boltzmann (IGLB) method has been proposed for threedimensional incompressible fluid flow simulation, for the first time. Equilibrium moments in moment space are derived from an incompressible BGKLB method. The incompressible Navier–Stokes equations can be recovered through the Chapman-Enskog multi-scale expansion without artificial compressible effects. To compare the performance of proposed model, several benchmark problems (such as a cubic lid-driven cavity flow, flow over a backward-facing step, and a double shear flow) are solved and the results are compared with those of both 19-bit Incompressible BGK Lattice Boltzmann (IBGKLB) method and existing CFD simulations. It is shown that the stability and accuracy of the 19-bit IGLB method is better than those of the 19-bit IBGKLB method; in fact with the IGLB model we can increase the Reynolds number by factor of 2.5 and still get stable results. The proposed 3-D IGLB method is successfully expanded and applied to simulation of the 3-D incompressible buoyancy driven flows. The results of the 3-D steady-state natural convection in an air-filled differentially heated cubic cavity obtained by the extended model comply well with the existing data in literature. In addition, natural convection from a discrete heat source which is mounted flush with the bottom wall of a horizontal enclosure is simulated. The obtained results indicate that the proposed method is very convenient for simulation of thermally driven flow problems.