The Lattice Boltzmann Method (LBM) is introduced in the Computational Fluid Dynamics (CFD) field as a tool for research and development, but its ultimate importance lies in various industrial and academic applications. Owing to its excellent numerical stability and constitutive versatility it plays an essential role as a simulation tool for understanding micro and macro fluid flows. The LBM received a tremendous impetus with their spectacular use in incompressible and compressible fluid flow and heat transfer problems. The applications of LBM to incompressible flows with simple and complex geometries are much less spectacular. From a computational point of view, the present LBM is hyperbolic and can be solved locally, explicitly, and efficiently on parallel computers. The present paper reviews the philosophy and the formal concepts behind the lattice Boltzmann approach and gives progress in the area of incompressible fluid flows, compressible fluid flows and free surface flows

This study involves the effect of adiabatic obstacles on two-dimensional natural convection in a square enclosure using lattice Boltzmann method (LBM). The enclosure embodies square-shaped adiabatic obstacles with one, two, and four in number. The single obstacle in cavity is centrally placed, whereas for other two configurations, a different arrangement has been made such that the core fluid zone is not hampered. The four boundaries of the cavity considered here consist of two adiabatic horizontal walls and two differentially heated vertical walls. The current study covers the range of Rayleigh number (103 ≤ Ra ≤ 106) and a fixed Prandtl number of 0.71 for all cases. The effect of size of obstacle is studied in detail for single obstacle. It is found that the average heat transfer along the hot wall increases with the increase in size of obstacle until it reaches an optimum value and then with further increase in size, the heat transfer rate deteriorates. Study is carried out to delineate the comparison between the presences of obstacle in and out of the conduction dominant zone in the cavity. The number of obstacles (two and four) outside of this core zone shows that heat transfer decreases despite the obstacle being adiabatic in nature.