A Review on the development of lattice Boltzmann computation of macro fluid flows and heat transfer

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.