| Lattice Boltzmann (LB) models are numerical schemes inspired by kinetic theory and are traditionally derived from conservation principles by using probabilistic concepts. In these models, macroscopic variables, such as density and momentum, are extracted by taking moments of discrete probability distributions near thermodynamic equilibrium. Although LB models are relatively simple, the numerical error introduced in the approximation of flow and transport in complex domains has not been fully characterized. Specifically, LB models have not been systematically studied in problems involving flow in domains with complex curved boundaries.; In this work, various systematic approaches are employed for deriving the truncation error of LB models which approximate Navier-Stokes flows. Improved LB models are formulated and validated through point-by-point comparison with limiting benchmark flows. Finally, the modified LB models are used to study a complex swirling flow in the strongly non-linear regime and to elucidate the physics of vapor-liquid flows near the critical point. The first case pertains to hydrodynamic instabilities occurring in the canonical Taylor-Couette-Poiseuille problem, and the numerical study serves to demonstrate the existence of a Stationary Helical Vortex mode. In the second flow, the LB simulations allow the study of the effect of interfacial mass transfer on the hydrodynamic stability of annular flow of near-critical CO2 in a microchannel. The LB results are corroborated by independent experimental data which serve to bolster the validity of the numerical schemes developed. |
