Developing a stable lattice Boltzmann method for computational fluid dynamics applications

The lattice Boltzmann method (LBM) has been employed to investigate the temporal and spatial characteristics of complex flows. Such complex flows include turbulent flows past cylinders confined in a channel, interfacial flows of two immiscible fluids and flows driven by density stratifications. Two dimensional and three dimensional thermal lattice Boltzmann models have been developed to study non-linear dynamics of these flows. Detailed formulations of the single relaxation lattice Boltzmann method are presented. Also presented by the present author are several variations of the lattice Boltzmann method. These methods include the multi relaxation lattice Boltzmann, regularized lattice Boltzmann and thermal lattice Boltzmann. Multi relaxation time converts velocity space to moment space, and regularized lattice Boltzmann uses the non-equilibrium parts of the stress. These methods are introduced to overcome stability problem of the lattice Boltzmann method. A unique lattice Boltzmann model that combines regularized and multi-relaxation time lattice Boltzmann method is introduced here to overcome the shortcoming of the lattice Boltzmann method. It is demonstrated here that the new model is stable for high speed turbulent flows. Turbulent flow structures predicted by the proposed method agree well with those observed by the experiments and those predicted by the large eddy simulations. Spatial resolution of the turbulence resolved here is equivalent to that obtained by direct numerical simulations. A two dimensional nine velocity and a three dimensional fifteen velocity lattice Boltzmann models have been employed to study interfacial flows. Body forces and interactive forces are included in these models. Several different approaches are adopted to handle different type boundary conditions imposed on the velocity and temperature fields. The nonlinear stages of Rayleigh Taylor instabilities and droplets rising in a stagnant fluid are characterized. The developed model shows and more stable more accurate results. The thermal model was employed to study the Rayleigh-Benard convection in a square and rectangular cavity. It has been demonstrated here that the lattice Boltzmann method can be an effective computational fluid dynamics tool to tackle complex flows.