【作者】 韦莺；

【导师】 陶建华；

【作者基本信息】 天津大学 ， 流体力学， 2008， 硕士

【摘要】 基于Boussinesq方程的波浪数学模型主要用来模拟水波在近岸浅水区的非线性变形,被广泛应用于海岸工程中。近几十年来,其数学模型本身和数值求解方法都得到了很大的发展。但是,这也使得求解此模型的计算量增大。单个处理器由于计算速度、内存以及存储空间的限制,已经不能满足工程实际计算的需要。本文基于这一实际情况,提出Boussinesq方程的一个区域分解并行算法。本文首先回顾了Boussinesq方程在色散性、非线性和浅化性方面的改进,以及并行算法在CFD领域的发展及应用,并对并行算法的分类、并行程序性能评价方法及MPI作了介绍。在提出并行算法之前,本文先介绍了所选用的Boussinesq方程模型、方程的差分格式、数值造波方法、边界处理方法以及串行算法求解过程。本文的并行算法采用了区域分解法,x方向计算时采用有重叠的区域划分,y方向计算时采用无重叠的区域划分,并通过Schwarz迭代法实现子区域之间的耦合。由于两个方向计算时都沿同一方向划分,避免了计算时不断进行方向的转换。对三个典型物理模型试验的模拟结果表明并行计算结果与串行计算结果吻合得很好,和试验结果一致,由此验证并行算法的正确性。本文还分析了该并行算法的加速比和效率,并讨论了重叠区域大小对计算时间的影响。更多还原

【Abstract】 The numerical models based on Boussinesq equations could simulate nonlinear wave deformations in coastal shallow waters. So such models have been widely used in coastal engineering. In recent decades, there has been a great improvement in Boussinesq equation and discrete scheme. At the same time, however, it makes model solving more complicated, and increases the amount of computation. Singer-processor computers can not meet the need of practical engineering computation with their limit on the processing speed and the size of local memory and storage. For this reason, a domain decomposition method for solving Boussinesq equation parallelly is proposed in this paper.Firstly, in this paper, the improvement of dispersive property, dissipative property, shoaling for the Boussinesq type equations, and the development of parallel methods in CFD are reviewed. Then, classification of parallel methods, performance analysis methods, and MPI are introduced. In order to propose the parallel method, some introduction about the model considered in this paper, finite difference scheme, method of wave generation, treatment of boundary and the process of serial simulation are described.In this paper, domain decomposition method is adopted for the parallel strategy, and subdomains are coupled with each other through Schwarz iterations. The global solution domain is partitioned into several overlapping subdomains in x direction computation, while partitioned into several non-overlapping subdomains in y direction computation. However, in both direction computations, partioning is carried out along only one dirction, which makes direction changing is avoided. The parallel strategy proposed in paper is used to simulate three experimental models. Comparion between parallel results, serial results and experimental data shows that parallel model tallies closely with serial model, and both of them agree with experimental data, which means that the parallel strategy is correct. Speedup and efficiency of the parallel strategy, and the effect of the overlapping amount is also analyzed.更多还原