In recent years, the Lattice Boltzmann method (LBM) has become attractive. Since the incompressible Navier–Stokes equations in theory and applications are important it is essential to develop a lattice Boltzmann Equation (LBE) which can precisely model the incompressible Navier–Stokes (NS) equations in general. It is well known that the small Mach number limit is equal to the incompressible limit, so it is possible to develop a LBE which can correctly model the incompressible NS equations only with the small Mach number limit. Compared to the equation-based approach, the method of LBE offers an alternative treatment for fluid dynamics. The LBE often employs uniform lattices to maintain a compact and efficient computational procedure, which makes it less efficient to perform flow simulations when there is a need for high resolution near the body and/or there is a far-field boundary. To resolve these difficulties, a multi-block method is developed. An accurate, conservative interface treatment between neighboring blocks is adopted, and demonstrated that it satisfies the continuity of mass, momentum, and stresses across the interface. Several test cases are employed to assess accuracy improvement with respect to grid refinement, the impact of the corner singularity, and the Reynolds number scaling. The present multi-block method can substantially improve the accuracy and computational efficiency of the LBE for viscous flow computations. From a computational view point, the notable advantages of LBM are its parallelism, simplicity of programming and ease of incorporating microscopic interactions. However, despite the notable success of the LBM, some shortcoming of the LB model are apparent. For instance the model may lead to numerical instability when the dimensionless relaxation time is close to 0.5. To overcome this shortcoming different method has been suggested like Multi Relaxation Time (MRT), Two Relaxation Time (TRT) and multi block. The MRT-LB model is of better numerical stability and has more degrees of freedom than the commonly used Single Relaxation Time (SRTLB) model. The main idea of the MRT-LB model is that the advection is mapped onto the momentum space by a linear transformation and the flux is still finished in the velocity space. Most of the existing MRT-LB models are constructed for the compressible NS equations in the low Mach number limit, and it is well understood that “compressible” error exits for simulating incompressible fluid flows. The recovered macroscopic equations from the existing MRT-LB model is the approximate incompressible NS equations through the Chapman–Enskog (CE) expansion. Considering the significance of the incompressible NS equations in theory and applications, it is necessary to establish an MRT-LB model which can exactly model the incompressible NS equations. In this work MRT, TRT and SRT models has been used to simulate cavity and flow on airfoil and studying stability of each one. Then for increasing the stability of each collision model they have been combined with a multi block method. Also using the multi block model for improve the stability, needs to identify area subjected to numerical instability in the computational domain. Another algorithm that has been introduced in this thesis is a combination of different collision models. namely multi collision. A comparison between its stability and that of the MRT, TRT and etc has been given. Keywords: Lattice Boltzmann, Stability Improvement, Multi Block, Multi Collision
