摘要虽然传统的基于网格的数值方法被普遍应用到计算流体力学及计算固体力 学领域，但在其诸多方面仍然存在很大的缺陷，导致这种方法在解决某些问题时 不能发挥很好的作用。而无网格方法的提出解决了这一难题。SPH 方法本身就是 一种典型的无网格数值方法，其具备自适应性、不受网格限制及拉格朗日特点。84141

本文以典型的方柱绕流为研究对象，基于 SPH 方法展开粘性流体绕流的研 究。利用流体动力学控制方程及虚粒子构筑边界的方法，完善了 SPH 程序模块。 分别分析了粒子的位置、速度等物理量，并与一般数值模拟方法相比较，结果认 为：

（1）SPH 方法对粘性流体绕流问题进行模拟是可行的，且相比于传统的基 于网格的方法，SPH 方法的模拟精度更高、细节处理更为妥善。

（2）在肯定 SPH 方法的优势的同时，要对其提出更高的要求。工程实验所 要解决的问题肯定是越来越为复杂的，因此 SPH 方法在计算精度、计算的稳定 性和计算的效率上仍不能满足实验的需要。

（3）SPH 方法在处理粒子总数保持不变的情况时极为方便，因为无论是固 壁边界还是镜像边界都能很好的防止实粒子的穿透。

（4）SPH 方法拥有十分广阔的发展前景，特别是对于解决更为复杂的流体 动力学问题极有帮助。

毕业论文关键词：光滑粒子流体动力学（SPH），数值模拟，粘度，方柱绕流。

Abstract Although traditional grid-based numerical methods are widely applied to computational fluid dynamics and computational solid mechanics, but in many    ways it still has a lot of deficiencies, what may result in this method is  not well playing  a role in solving some of the problems。 But at the same time the grid  method  is proposed to solve this problem。 SPH method is a typical meshless numerical method, comprising adaptability, without restrictions and grid Lagrange features。

In this paper, the typical flow around square cylinder as the research object, the viscous fluid flow around expansion based on SPH method。 Using fluid dynamics equations and boundary build virtual particles, improve the SPH program modules。 Were analyzed particle position, velocity and other physical quantities, and compared with the general method of numerical simulation, concluded that:

(1)SPH method to the viscous fluid flow around simulation is feasible, and compared to traditional grid-based method, higher precision SPH simulation methods, details of the deal is more appropriate。

(2)In the affirmative, while the advantages of SPH method, you want to put forward higher requirements。 Engineering experiments to solve the problem is definitely more complex, so the SPH method in accuracy, stability and computational efficiency calculation still can not meet the needs of the experiment。

(3)SPH method in dealing with the situation remains the same total number of particles is extremely convenient, because both the wall boundary or border can be a good mirror to prevent the penetration of solid particles。

(4)SPH method has a very broad prospects for development, especially very helpful to solve more complex fluid dynamics problems。

Keywords: smoothed particle hydrodynamics (SPH), numerical simulation, viscosity, flow around square cylinder。

目录

第一章 绪论 1

1。1 选题背景及意义 1

1。2 数值模拟 2

1。2。1 数值模拟的作用 2

1。2。2 数值模拟一般的求解过程 3

1。3 基于网格方法和无网格方法