【作者】 王兴勇；

【导师】 索丽生；

【作者基本信息】 河海大学 ， 水利水电工程， 2003， 博士

【摘要】 Lattice Boltzmann(LB)方法是二十世纪八十年代中期发展起来的一种流场模拟方法。与传统的计算方法如FEM、FDM等相比，LB方法具有算法简单、编程容易、压力可以通过状态方程直接求解、能够模拟各种复杂边界的流场等优点，并且计算的局域性使其在并行计算方面也具有很大的优势。目前，LB方法已经在水力学、多相流、多孔介质流、热传导以及磁流动力学等领域取得了丰硕的成果，展示了广阔的应用前景，它将成为传统计算方法的有力竞争者。为了消化和吸收近年来LB方法在理论和应用方面的新成果，探索在水力计算方面的新途径以促进LB方法实用化的发展，本文进行了下列研究工作： 综述了LB方法在理论研究和实际应用方面的新进展，以及D2Q9模型的推导过程和其他一些常用的模型； 在水动力边界条件和通用边界条件的基础上提出了一种新的联合边界条件方法，它综合了上述两种边界条件的优点，在流场的各种边界处理中取得了非常好的效果，经过模块化的处理以后这种边界条件具有更好的实用性； 针对均匀网格的LB方法计算效率较低的不足，提出了双重网格的Lattice Boltzmann方法，通过二维Poiseulle流动、后台阶流动和渠道方槽流动三个算例的模拟，证明这种方法能够明显地提高流场模拟的计算效率； 此外，根据复杂区域流场的特征提出了Lattice Boltzmann方法的分块-耦合算法，利用LB方法的计算特性实现块与块之间的数据交换，充分利用计算资源提高计算效率，通过对“T”型、“十”型和“X”型分岔管道流场的模拟，展示了这种算法的特征和优点，以及它所具有的应用前景。 通过本文的研究，可得出如下结论：LB方法的模型在接近不可压缩的条件下能够以二阶精度逼近N-S方程；LB方法理论的完善能够有效地提高流场模拟的计算效率；并行计算的发展有利于LB方法模拟大尺度的复杂流场。以后有待深入研究的问题是增强方法的稳定性、提高模拟流场的雷诺数、曲线边界的处理和实用化的进一步发展。更多还原

【Abstract】 Lattice Boltzmann (LB) method was developed into a flow-field simulating scheme in the middle of 1980s. Compared with traditional numerical methods such as the FEM, FDM, etc, the LB method has several important features, including: simplicity in algorithm, easily programming, direct calculation of pressure from a state equation and amenability to simulate all kinds of flow field with complex boundaries, it also has much advantage in the respect of parallel computation because of its regional evolution. In recent years, plentiful and substantial fruits achieved by the LB method in simulations of hydraulics, multiphase flows, flows in porous media and heat transfer as well as magnetohydrodynamics, have revealed a broad perspective of application of this method, it will become a powerful competitor to the conventional approaches. In order to absorb the recent achievement in theory and application of the LB method, explore new ways in hydraulic computation to promote the development of practice, some work is carried out in this thesis, as following:Advances in the theory research and application, deductive process of the D2Q9 model and some other commonly used models of the LB method are summarized.Based on the hydrodynamic and general boundary conditions, a new joint boundary condition is presented, it integrates advantage of the two conditions above and obtains very good results in dealing with all kinds of boundaries of flow fields. This boundary condition becomes more applicable after treatment of being modularized.Aiming at the defect of low computational efficiency in the uniform-mesh LB method, a new double-mesh Lattice Boltzmann method is put forth and three numerical examples, two-dimensional Poiseulle flow, backward-facing step flow and flow in channel with a rectangular slot, are simulated, proving this method can obviously enhance the computational efficiency.In addition, according to the character of flow field in complex region, a new decomposition-couple algorithm of the Lattice Boltzmann method is put forward, itmakes good use of character of the LB method to implement data exchanges between divided regions, sufficiently utilizes the computational resource to increase computational efficiency. Then, fork pipelines with "T", "+" and "X" geometries are simulated, depicting the character and merits of this algorithm, as well as its perspective in application.Through the research in this thesis, following conclusion can be drew: on the condition of nearly incompressible limit, the N-S equations can be recovered by the LB method’s models with 2-order numerical precision; computational efficiency in simulating flow fields can be improved effectively by perfection of the LB method’s theory; development of parallel computation can contribute to the simulation of large-scale flow field with complex geometry. In the future, some issues need to be investigated further, which include: enforcement of the stability, raising Reynolds number of the flow field being simulated, treatment of curve boundaries as well as further development of application.更多还原