【作者】 王超；

【导师】 陈红全；

【作者基本信息】 南京航空航天大学 ， 流体力学， 2008， 硕士

【摘要】 本文对格子Boltzmann方法的基本思想与发展历史进行了阐述,包括对格子Boltzmann方程与N-S方程的关系进行的推导与分析,其研究主要是围绕格子Boltzmann方法的理论与应用展开的。采用格子Boltzmann方法需要构造粒子速度模型。文中首先对两种常用的二维粒子速度模型D2Q9与D2Q13进行了分析与比较,并基于这两种模型研制了对应的计算程序,成功地模拟出不同雷诺数情况下的二维驱动空腔流动;接着,对格子Boltzmann方法中涉及的各种边界处理方法做了详细的分析,结合非均匀网格的格子Boltzmann方法—TLLBM,给出了推导过程,然后用此种方法编程模拟了圆柱及二维翼型这两种曲面边界的绕流问题;最后,介绍了格子Boltzmann方法中常见的流动模型,其中重点对IEDDF热模型进行了分析,并选用二维封闭空腔自然对流进行了具体的数值模拟。文中展示了上述典型流动问题的数值模拟结果,并在相关结果图中给出文献结果供比较。更多还原

【Abstract】 Lattice Boltzmann method (LBM) is studied in this dissertation for solving fluid flow problems. The basic concept of the method is firstly described, and its history of development is briefly reviewed. In order to solve the viscous flow problems which are governed by the macroscopic Navier-Stokes Equations, a detailed investigation including the principle and application of LBM is presented.When the flow problems are solved by LBM, the particle velocity model is usually required to accomplish the simulation. Therefore two particle velocity models named as D2Q9 and D2Q13 are firstly analyzed and compared, and then they are implemented in the framework of LBM to simulate 2D lid driven cavity flows; as the uniform grid is used by the traditional LBM, it encounters difficulties when dealing with complicated configurations represented by curved boundaries. In order to overcome this difficulty, a new method named as TLLBM which uses non-uniform grid is proposed. The new method is applied to solve the flows over a cylinder and NACA0012 airfoil in the present work; Furthermore, some popular models for LBM are described in the dissertation, and special attention is paid to the IEDDF thermal model that is implemented to simulate 2D cavity nature convection flows.A comparison between the numerical results and the reference works is made, and they agree well with each other.更多还原