【作者】 倪歆韵；

【导师】 陶建华；

【作者基本信息】 天津大学 ， 流体力学， 2007， 硕士

【摘要】 Boussinesq方程是用于描述非线性色散波在浅水中传播的方程,以Boussinesq方程为基础的数学模型可以用来模拟复杂地形上波浪的传播情况以及波浪与结构物之间的相互作用,它可以模拟波浪的折射、绕射、反射及浅化等现象,因此在工程中具有广泛的应用。随着Boussinesq方程的不断改进,Boussinesq方程已经能进行深水区和大面积场的计算,但是受到计算机存储空间及CPU的限制,使用单个处理器计算已经不能满足工程实际的需要,本文从这一实际情况出发,进行Boussinesq方程的并行程序设计,结合高性能并行计算机集群系统来进行Boussinesq方程水波数值模拟计算。本文首先综述了Boussinesq方程在色散性、非线性等方面的改进,回顾了并行算法在Boussinesq方程中的应用,介绍了并行计算的分类和性能分析的方法。本文采用的方程是Madsen和Sch?ffer(1995)推导所得的方程,该方程具有很好的色散性,能适用于变水深、斜坡等复杂地形。对该方程在空间上采用了中心紧致差分格式,时间上采用中心差分格式,使得在差分点个数不变的情况下取得了更高的精度。方程的求解采用ADI方法,使得方程的求解具有很好的稳定性。本文采用了MPI+Fortran的并行程序语言编写程序,程序具有很好的可移植性。对该方程采用了区域分解的并行算法进行并行程序设计,在不同方向计算时进行不同的区域划分,在进行模型并行化的过程中考虑了进程的负载平衡、死锁的避免、虚拟进程的设置等问题,进程间的数据交换通过消息的发送和接收来进行,经模型验证并行程序计算结果和串行程序的计算结果是完全吻合的,并在一定程度上缩短了计算时间。更多还原

【Abstract】 Boussinesq equation is a nonlinear dispersion wave equation in shallow water. The numerical models based on Boussinesq equations could simulate the sitution of waves propagate on uneven bottom and the influence between waves and structure. It could simulate refraction, diffraction, reflection, shoaling etc. Therefore, Boussinesq equation models have been used widely. Along with continuous improvement of Boussinesq equation, it could simulate deep water region and great area field, however, computing only by one processor could not statisfy the projects’actual need because of the limitation of the memory’s size and CPU’s speed of computer. In this thesis, it designs parallel program of Boussinesq equation in order to solve this problem, and utilizes high performance parallel machine cluster system to Boussinesq equation’s wave simulation.In this thesis, the improvements of dispersive property, shoaling, the application of parallel metods of Boussinesq equations are reviewed. Then Parallel machine classification and performance analysis method are introduced. It adopts the Boussinesq equation set up by Madsen and Sch?ffer(1995). This equation has better dispersive property than ever; it can be used on terrain of changed depth of water and slope. The center compact difference in space and center difference in time are applied in Boussinesq equation. As a result, it can obtain higher precision than the center difference in space while the number of difference points is not changed. ADI method is applied while solving this difference equation. It ensures that the solution process is stable.MPI+Fortran parallel program language is used in this paper. The program has good portability. Adopting region decomposition method to design parallel program, the thesis uses different decomposition region at the different computation direction. It considers the load balance, avoiding dead lock, setting dummy processor and so on. The data’s exchange among processors uses“send and receive”method. At last, this parallel program is confirmed by models, the result of calculation tallies with the serial result. Paralle program reduces the computing time in a certain degree.更多还原