Navier Stocks Equations are being used for years in fluid Dynamics as the basic equations. There are almost three decades that the most basic equations of Lattice Boltzmann are growing their usage from fundamental science like Physics and Mathematics to more applicable knowledge which is engineering. The reason of this growing is the need of more precise solution for Micro- and Nano-scale fluid flows. After that, Lattice Boltzmann Method (LBM) has been used in different areas of Fluid Dynamics. Then, the vast effort for improving this method leads to invention of Multi-block LBM, in the recent years. The Standard LBM uses a uniform mesh in the whole domain; therefore when more accuracy is needed in some special parts of the domain, the whole domain’s mesh should be made finer. This causes an exponential growth in the computational cost, which its rate is the ratio of lattice space between two mesh-systems. To resolve this problem, in the Multi-Block LBM, a domain is divided into some independent blocks which could have different sizes. Therefore, in the place where gradients are higher and therefore finer mesh is needed, a local mesh refinement could be applied only to the desired blocks. For applying this method to fluid mechanics, in present work, some benchmark problems have been used. Each benchmark has its own property which needs special care in applying this method. At first the lid-driven cavity fluid flow has been studied. Then the transient fluid flow around a cylinder in 2D channel has been solved. As a last example, the flow through a backward facing step is simulated. In each problem, there are some parameters which could be used as the comparing quantity. In all of these benchmarks the multi-block results agree well with these obtained using standard LBM. In some cases great improvement in accuracy was observed.
