基于SPH的无网格算法研究及其在水轮机流场计算中的应用

发布时间：2018-04-04 03:14

本文选题：SPH　切入点：Geohash　出处：《上海交通大学》2014年硕士论文

【摘要】：光滑粒子动力学算法（SPH）作为最早出现的无网格算法之一，是一种完全无网格的拉格朗日粒子算法。SPH算法将流场用粒子群来表示，，每个粒子携带自身所在位置的速度、压力、温度、密度等流场信息。该算法采用光滑核近似和粒子近似对Navier-Stokes方程进行离散，并将偏微分方程组转化为常微分方程组，进而得到离散代数方程组，通过求解得到每个粒子点的信息。由于该算法是完全无网格的基于粒子的方法，因此不存在网格的扭曲和重构问题，在求解自由液面和大变形问题中有较大优势。本文以SPH算法为研究对象。重点研究了影响该算法计算效率的搜索问题，在充分分析常用的两种搜索方法基础上，将用于地图搜索的Geohash算法引入到SPH算法中，采用新的编码方式将二维的坐标转化为一位字符串形式进行保存。通过对比字符串的相同位数来获取计算点粒子支持域内的最近粒子。在对不同的粒子数的对比实验中可以看出，Geohash算法的效率远高于全配对搜索算法和链表搜索算法。本文基于改进后的SPH算法编制了计算程序，并用液滴的自由坠落和经典溃坝模型检验了改进算法以及程序的计算精度。从计算结果可以看出，改进算法能够很好模拟自由液面问题。进一步将改进SPH算法应用于二维和波浪水槽的模拟中，分别模拟了不同波长和振幅的线性单色波，模拟实验结果能够很好的理论解相吻合。本文还将SPH算法应用于开口系统的二维水轮机模拟中，首先建立了速度入口边界和压力出口边界的SPH算法模型，并对这两种模型进行了验证。进一步将这两种开口边界应用于二维水轮机的模拟中。通过和相关实验的对比发现，SPH能够得到和实验相当精度的计算结果。
[Abstract]:As one of the earliest meshless algorithms, the smooth particle dynamics algorithm (SPH) is a completely meshless Lagrange particle algorithm. The SPH algorithm uses particle swarm optimization to represent the flow field, and each particle carries the velocity and pressure of its own position.Flow field information such as temperature and density.In this algorithm, the smooth kernel approximation and particle approximation are used to discretize the Navier-Stokes equation, and the partial differential equations are transformed into ordinary differential equations, and then the discrete algebraic equations are obtained, and the information of each particle point is obtained by solving the equations.Because the algorithm is a completely meshless particle based method, there is no mesh distortion and reconstruction problem, so it has a great advantage in solving free liquid surface and large deformation problems.In this paper, SPH algorithm is taken as the research object.This paper focuses on the search problem which affects the computational efficiency of the algorithm. Based on the analysis of two common search methods, the Geohash algorithm for map search is introduced into the SPH algorithm.A new encoding method is used to transform the two-dimensional coordinates into one-bit string for preservation.The nearest particles in the compute point particle support domain are obtained by comparing the same number of bits of the string.The comparison of different particle numbers shows that the efficiency of Geohash algorithm is much higher than that of full pair search algorithm and linked list search algorithm.In this paper, based on the improved SPH algorithm, a calculation program is developed, and the improved algorithm and the calculation accuracy of the program are tested with the free drop of droplets and the classical dam-break model.It can be seen from the calculation results that the improved algorithm can well simulate the free surface problem.Furthermore, the improved SPH algorithm is applied to the simulation of two-dimensional and wave flume. The linear monochromatic waves with different wavelengths and amplitudes are simulated respectively. The experimental results are in good agreement with the theoretical results.In this paper, the SPH algorithm is also applied to the two-dimensional turbine simulation of open system. Firstly, the SPH algorithm model of velocity inlet boundary and pressure exit boundary is established, and the two models are verified.The two open boundaries are further applied to the simulation of two-dimensional hydraulic turbines.By comparing with the related experiments, it is found that the SPH can obtain the equivalent accuracy of the experimental results.
【学位授予单位】：上海交通大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：TK730

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