摘要光滑粒子流体动力学（Smoothed Particle Hydrodynamics ，SPH）方法作为最早 出现的无网格算法，在 40 多年的发展中其应用领域越来越广泛。核函数作为 SPH 方法中一个重要组成部分，在积分近似法（即场函数近似法），粒子近似法这两个 重要步骤中起着不可忽视的作用。为此，本文研究了不同核函数对光滑粒子流体动 力学的计算结果的影响。83976

本文以三次样条函数，高斯型核函数，五次样条函数以及新四次样条函数为研 究对象，将这些核函数应用到 SPH 方法的计算模块之中，分别对剪切流和泊肃叶流 这两种典型流动进行计算，得到了计算结果。通过对计算结果中的粒子分布图，速 度等值图以及粒子速度分布图等进行分析，得到如下结论：

（1）高斯型核函数有着稳定性高和精度高的优点，所得光滑粒子 SPH 计算结 果与实际流动计算结果十分地符合。运用高斯型函数作为 SPH 法的核函数，其流体 粒子不会出现游离现象且粒子速度方向与实际流动方向较为贴近。

（2）三次样条函数作为 SPH 的核函数，其计算结果在精度与准确性较高斯型 函数稍差些，但从总体来说还是与实际流动特征基本一致。

（3）五次样条函数对流体力学问题进行模拟时可能会出现个别粒子游离与集 体粒子之外的现象。但流动的一些特征还是能表现出来。

（4）新四次函数不适用于 SPH 方法中。它不仅需要耗费大量的计算时间才能 发生明显的粒子位移，且其所得粒子分布与速度分布和实际流动的有着非常大的差 距。

毕业论文关键字：光滑粒子流体动力学；核函数；无网格法

Abstract The smooth particle hydrodynamics method as the earliest meshfree algorithm, in the development of more than 30 years of its application field is more and more widely。Kernel function, as an important part of SPH method, the integral approximation function approximation (game), particle approximation method of these two important step plays a role can not be ignored。To this end, this paper studies the different kernel function to the influence of the smooth particle hydrodynamics calculation results。

Based on cubic spline function, Gauss kernel function, five times spline function, and the new four times spline function as the research object, the kernel function is applied to the calculation module of SPH method, respectively, the Shear flow and the Poiseuille flow, these two kinds of typical flow calculation results are obtained。Based on the calculation results of particle distribution, speed contour and particle velocity distribution were analyzed, and get the following conclusion:

(1)Gauss kernel function has the advantages of high stability and high precision, smooth SPH particles calculation results and the actual flow calculation results accord with very。Using the Gauss function as the kernel function of SPH method, the phenomenon of fluid particles will not be free and particle velocity is relatively close to the direction and the actual flow direction。

(2)The cubic spline function as the kernel function of SPH, the calculation results in the precision and accuracy Gauss function is a bit poor, but from the overall is consistent with the actual flow characteristics。

(3)Quintic spline function to simulate the convection strength problem may occur when the outside of the inpidual and collective free particles。But still can show some flow characteristics。

(4)The new four function does not apply to SPH method。It not only requires a lot of time to happen obvious particle displacement, and the income distribution and velocity distribution of particles and the actual flow has a very big gap。

Keywords:Smooth particle hydrodynamics;Kernel function;Meshfree method