本文選題：SPH　切入點(diǎn)：Geohash　出處：《上海交通大學(xué)》2014年碩士論文

【摘要】：光滑粒子動(dòng)力學(xué)算法（SPH）作為最早出現(xiàn)的無(wú)網(wǎng)格算法之一，是一種完全無(wú)網(wǎng)格的拉格朗日粒子算法。SPH算法將流場(chǎng)用粒子群來(lái)表示，，每個(gè)粒子攜帶自身所在位置的速度、壓力、溫度、密度等流場(chǎng)信息。該算法采用光滑核近似和粒子近似對(duì)Navier-Stokes方程進(jìn)行離散，并將偏微分方程組轉(zhuǎn)化為常微分方程組，進(jìn)而得到離散代數(shù)方程組，通過(guò)求解得到每個(gè)粒子點(diǎn)的信息。由于該算法是完全無(wú)網(wǎng)格的基于粒子的方法，因此不存在網(wǎng)格的扭曲和重構(gòu)問(wèn)題，在求解自由液面和大變形問(wèn)題中有較大優(yōu)勢(shì)。 本文以SPH算法為研究對(duì)象。重點(diǎn)研究了影響該算法計(jì)算效率的搜索問(wèn)題，在充分分析常用的兩種搜索方法基礎(chǔ)上，將用于地圖搜索的Geohash算法引入到SPH算法中，采用新的編碼方式將二維的坐標(biāo)轉(zhuǎn)化為一位字符串形式進(jìn)行保存。通過(guò)對(duì)比字符串的相同位數(shù)來(lái)獲取計(jì)算點(diǎn)粒子支持域內(nèi)的最近粒子。在對(duì)不同的粒子數(shù)的對(duì)比實(shí)驗(yàn)中可以看出，Geohash算法的效率遠(yuǎn)高于全配對(duì)搜索算法和鏈表搜索算法。 本文基于改進(jìn)后的SPH算法編制了計(jì)算程序，并用液滴的自由墜落和經(jīng)典潰壩模型檢驗(yàn)了改進(jìn)算法以及程序的計(jì)算精度。從計(jì)算結(jié)果可以看出，改進(jìn)算法能夠很好模擬自由液面問(wèn)題。進(jìn)一步將改進(jìn)SPH算法應(yīng)用于二維和波浪水槽的模擬中，分別模擬了不同波長(zhǎng)和振幅的線性單色波，模擬實(shí)驗(yàn)結(jié)果能夠很好的理論解相吻合。 本文還將SPH算法應(yīng)用于開(kāi)口系統(tǒng)的二維水輪機(jī)模擬中，首先建立了速度入口邊界和壓力出口邊界的SPH算法模型，并對(duì)這兩種模型進(jìn)行了驗(yàn)證。進(jìn)一步將這兩種開(kāi)口邊界應(yīng)用于二維水輪機(jī)的模擬中。通過(guò)和相關(guān)實(shí)驗(yàn)的對(duì)比發(fā)現(xiàn)，SPH能夠得到和實(shí)驗(yàn)相當(dāng)精度的計(jì)算結(jié)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.
【學(xué)位授予單位】：上海交通大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2014
【分類號(hào)】：TK730

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本文編號(hào)：1708121