光滑粒子流体动力学（Smoothed Particle Hydrodynamics，简称为 SPH）方法是一种拉格朗日型无网格方法，此方法由 Lucy 和 Gingold 等人在 1977 年首次提出。与基于网格的数值方法相比，SPH 方法完全不依赖于网格，并且具有 Lagrangian 特性、质点特性和自适应特性等优点，因此非常适合大变形、自由表面流动等复杂界面问题的数值模拟。 但 SPH 方法在处理自由表面流问题时存在计算量大、耗时长的问题，因此有必要对其进行并行化处理。本论文主要工作如下：
（1）针对 SPH 方法处理自由表面流问题时计算效率低的问题，比较与改进了 SPH方法的某些数值处理技术。首先，发展了链表搜索算法，用于搜索最近相邻粒子。通过 对二维液滴撞击固壁面问题进行数值模拟，结果表明基于链表搜索法的 SPH 方法效率更高。其次，提出了一种由固壁粒子和固壁边界外虚粒子耦合的加强型边界处理方法。结果表明该方法不仅可以阻止临近固壁边界的流体粒子穿透固壁面，而且还能够显著减少 SPH 数值模拟所消耗的计算时间。
（2）针对 SPH 方法存在的计算量大、耗时长的问题，提出了基于粒子分解的 SPH并行算法。该并行算法的基本思想是将所有粒子平均分配到各个进程进行计算，每个时间步通信仅调用一次发送、接收和广播函数，因此编程易于实现，且可扩展性良好。应 用该并行算法数值模拟二维溃坝问题和二维液滴撞击固壁面问题，结果表明本论文提出的基于粒子分解的 SPH 并行算法不仅能够有效模拟自由表面流问题，而且还能大范围缩减 SPH 方法数值模拟的计算时间。
（3）针对 SPH 方法数值模拟局限于二维空间的问题，本论文将第三章提出的加强 型边界处理方法和第四章提出的并行算法推广应用到三维问题的数值模拟中。分别对三维溃坝问题以及三维液滴冲击液膜问题进行数值计算，分析了进程数、粒子数、并行效 率和加速比之间的关系，结果表明本论文提出的加强型边界处理方法和基于粒子分解的并行算法对于 SPH 方法在处理大规模自由表面流问题时，能够大幅度减少数值模拟所消耗的计算时间。
本论文基于消息传递接口（Message Passing Interface，简称为 MPI）并行程序设计平台，以 C++语言作为算法实现的编程语言，设计了基于粒子分解的 SPH 并行算法。 应用该并行算法对典型二维、三维溃坝以及液滴问题进行数值模拟，分析了进程数、粒子数、并行效率和加速比之间的关系。结果表明，当粒子数大于百万时，最大加速比可达 30 以上。因此，本论文提出的基于粒子分解的 SPH 并行算法可以为大规模三维问题的数值模拟提供一种高效、准确的计算工具。

The Smoothed Particle Hydrodynamics (SPH) method is a Lagrangian meshless method, which was first proposed by Lucy and Gingold et al. in 1977. Compared with grid-based numerical methods, the SPH method is completely grid-independent and has the advantages of Lagrangian properties, mass point properties and adaptive properties. Therefore, it is very suitable for numerical simulation of complex interface problems such as large deformation and free surface flow. However, the SPH method suffers from the problems of large computational volume and time consuming when dealing with free surface flow problems, so it is necessary to parallelize it. The details in this thesis are as follows:
(1) In this thesis, certain numerical techniques of the SPH method are compared and improved to resolve the problem of low computational efficiency of the SPH method when dealing with free surface flow problems. First, a linked list search algorithm is developed to search the neighboring particles. Through numerical simulations of the two-dimension aldroplet impinging on the solid wall surface problem, the results indicate that the SPH method based on the chain table search method is more efficient. Second, an enhanced boundary treatment method coupled by solid wall particles and imaginary particles outside the solid wall boundary is proposed. The results indicate that this method can not only prevent the fluid particles near the solid wall boundary from penetrating the solid wall surface, but also significantly reduce the computational time consumed by the SPH numerical simulation.
(2) In this thesis, the SPH parallel algorithm based on particle decomposition is proposed to resolve the problems of large computation and time consuming of SPH method. The basic idea of this parallel algorithm is to distribute all particles equally to each process for computation, and each time-step communication only calls the send, receive and broadcast functions once. Therefore, the programming is easy to implement and has a good scalability. The parallel algorithm is applied to simulate the two-dimensional dam-break problem and the two-dimensional droplet-impacting solid wall surface problem, and the results indicate that the particle decomposition-based SPH parallel algorithm proposed in this thesis can not only effectively simulate the free surface flow problems, but also reduce the computational time of 
the SPH simulation on a large scale.
(3) In this thesis, the enhanced boundary treatment method proposed in Chapter 3 and the parallel algorithm proposed in Chapter 4 are extended and applied to the numerical simulation of three-dimensional problems to solve the problem that the numerical simulation of SPH method is limited to two-dimensional space. The relationships between the number of processes, the number of particles, the parallel efficiency and the acceleration ratio are analyzed for the three-dimensional dam-break problem and the three-dimensional droplet impact liquid film problem, respectively. The results indicate that the enhanced boundary treatment method and the particle decomposition-based parallel algorithm proposed in this thesis for the SPH method can significantly reduce the computational time consumed by the numerical simulation when dealing with large-scale free surface flow problems.
This thesis is based on the Message Passing Interface (MPI) parallel programming platform. The SPH parallel algorithm based on particle decomposition is designed using C++ as the programming language for algorithm implementation. The parallel algorithm is applied to numerical simulations of typical two-dimensional and three-dimensional dam-break and droplet problems, and the relationship between the number of processes, the number of particles, the parallel efficiency and the acceleration ratio is analyzed. The results reveal that the maximum acceleration ratio can be more than 30 when the number of particles is greater than one million. Therefore, the SPH parallel algorithm based on particle decomposition proposed in this thesis can provide an efficient and accurate computational tool for the numerical simulation of large-scale three-dimensional problems.

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