基于不同网格结构的LBM算法研究

THE NUMERICAL STUDY OF LATTICE BOLTZMANN METHOD BASED ON DIFFERENT GRID STRUCTURE

传统的格子波尔兹曼方法(lattice--Boltzmann method,LBM)通常基于标准均匀网格,这主要取决于速度的空间离散格式.均匀网格结构的特点,使LBM在处理具有复杂边界的问题时遇到较大的困难,从而限制了它的应用.另外,对于较为复杂的流动,其流场存在流动变化剧烈和平缓的区域,在流动变化剧烈的区域,往往需要足够的网格点才能更好地捕捉到流场信息,而均匀网格会使得网格数量过多,这会增加计算量,但网格数量过少又无法获得必要的流场信息,使LBM的计算效率降低.为了解决上述问题,用不同的网格结构,以顶盖驱动的腔体内流、柱体绕流和翼型绕流为例,探讨了提高LBM算法的计算效率和适用性问题.

In this paper, we mainly focus on the different grid structures used in lattice Boltzmann method （LBM）. We present corresponding methods for each grid structure. As we know, in the numerical simulations based on the traditional LBM, the standard uniform grid is always hired. This is up to the discrete velocities on the grid node. Yet, it is a thomy question when the LBM is employed to solving problems with complex boundaries, due to the grid structure of standard uniform grid itself. And this shortcoming would decrease the applicability of LBM. Besides, for those complicated flows, it is necessary to have enough meshes to capture the flow information in the zones where the flow state changes fiercely. In another word, if there are too many grids, it will greatly enlarge the computational burden with the use of standard uniform grid. On the other side, if the grids are not enough, it is hard to get a satisfied result. This dilemma greatly decreases the efficiency of LBM. For solving those questions above, we use different grid structures to improve the applicability and efficiency of LBM. In this paper, we perform the simulations of the lid-driven flow of cavity, flow around cylinder and flow around airfoil as our numerical cases.