Debanik Bhattacharjee
Based on the kinetic theory, Lattice Boltzmann methods were proposed to address the shortcomings of the lattice-gas automation. In traditional computational fluid dynamics methods (CFD), Navier–Stokes equations (NS) solve mass, momentum and energy
conservation equations on discrete nodes, elements, or volumes. In other words, the nonlinear partial differential equations convert into a set of nonlinear algebraic equations, which are solved iteratively. In LBM, the fluid is replaced by fractious particles. These particles stream along given directions (lattice links) and collide at the lattice sites. The LBM can be considered as an explicit method. The collision and streaming processes are local. Hence, it can be programmed naturally for parallel processing machines. Another beauty of the LBM is handling complex phenomena such as moving boundaries (multiphase, solidification, and melting problems), naturally, without a need for face tracing method as it is in the traditional CFD.
This method naturally accomodates a variety of boundary conditions such as the pressure drop across the interface between two fluids and wetting effects at a fluid-solid interface. It is an approach that bridges microscopic phenomena with the continuum macroscopic equations. Further, it can model the time evolution of systems.
A survey is done of the most significant developments in LB methods. Some of the latest trends is the entropic LB method and the applications in the domain of turbulent flow, deformable particle and fibre suspensions. Some examples are presented to highlight the scalability of LB methods for parallel processing.