【作者】 涂运冲；

【导师】 吴克启；

【作者基本信息】 华中科技大学 ， 流体机械及工程， 2013， 博士

【摘要】 得益于计算机技术发展,科学计算得到了飞速的发展。目前,人们研究噪声机理的手段有实验、理论分析以及数值计算。气动声学研究一般是从宏观的角度展开的,本论文在Hamilton体系下,从宏观和微观相关联的角度研究声波在气体介质中的传播问题,并在求解波动方程过程中,引入了与现有差分算法不同的辛算法。辛算法相对传统算法有其独特的优越性,因为保守体系可用Hamilton体系的方法描述,其特点是保辛。保辛给出保体系结构最重要的特性。而对于某些非保守系统则也可通过转化为保守系统进行分析。与现有差分算法不同的是,辛算法具有保辛性,保辛性也是保体系结构最重要的特性。而对于非保守系统,则可通过转化,将它专为保守系统进行研究。数值算例分析表明,与同阶的有限差分格式相比较,本文给出的辛算法在效率上和精度上有较大的优势。在Hamilton体系下,利用辛算法分析并求解了气动声学经典波动方程。首先建立一个在离散化网格上的准粒子体系,引入准粒子间相互作用势,用Hamilton力学描述这个在时间上连续而空间上离散的体系,准粒子按照Hamilton正则方程运动。推导演绎了Hamilton描述、辛算法及波动方程之间的联系及准粒子体系的互作用系数。通过数值算例分析,验证了本文算法的正确性和稳定性。文中应用辛算法数值模拟了声在空气中的传播。从数值模拟的结果来看,用Hamilton系统方法来描述声波的传播是有效的。同时对应的保结构辛算法也可以直接应用于数值模拟,它比耗散型格式的计算结果更为符合物理实质,也更为精确。由于微观体系粒子的能级与粒子配分函数之间存在特定的关系,而由配分函数可以求出体系的内能、熵、自由能等等热力学量,进而可获得气动声场的声压等宏观参数。在Hamilton体系下,分别以量子力学的不同表述形式构建模型研究声的传播问题。即分别以波动力学核心的Schrodinger方程为粒子运动控制方程,结合群论、配分函数以及路径积分方法关联配分函数,构建新模型来研究声的传播。数值计算结果表明,这两种模型都能用来分析气动声场。本文的方法研究及其应用,为气动声学的研究提供了新的途径。更多还原

【Abstract】 Due to the development of computer ability, The computational seience got a fast developing. There are the three means to understand the mechanism of aeroacoustics that its the method of theoretical study, experiment and numerical simulation.Conventional study of aeroacoustics is conducted under the system of Newtonian mechanics. The doctoral thesis study the propagation of sound waves in a gas medium by contacting the macro and micro perspectives in the Hamilton framework, and solve the wave equation in the process of introducing symplectic. Difference from the traditional algorithms, the symplectic algorithm has mang advantages. the most of these advantages is the conservation of symplecticness, which is the most important feature of conservative systems can be described with the Hamilton system, and its characteristic is the conservation of symplecticness. Symplectic algorithms can handle some non-conservative systems through converting inio the conservative system. Numerical examples show that: comparing with the same order finite difference scheme, symplectic algorithms used by this doctoral thesis have a greater advantage in efficiency and accuracy,the Hamilton theory framework is adopted in this dissertation to analyze the problems of acoustic wave propagation in air, to study the propagation of stimulation acoustic waves, and to explore new approaches to research on aeroacoustics. A quasi-particle system on a discrete lattice is built up first, and the interaction potential among quasi-particles is then determined. This system, which is continuous in time while discrete in space, is expressed in terms of Hamilton mechanics, and the motion of quasi-particles is governed by Hamilton canonical equations. Based on the basic principle of Hamilton mechanics, the relationships between the symplectic algorithms and the the wave equation and interaction coefficient s of quasi-particle system are derived. The numerical simulation results suggest that the Hamilton method is effective in describing the propagation of acoustic waves. The corresponding conserving symplectic algorithm can also be directly applied in numerical simulations, the results of which are not only more consistent with physical essence but are also more accurate than those of a dissipative scheme.Since there is a specific relationship between the energy levels of the micro-system particle and particle distribution function,the thermodynamic quantities which contains the internal energy of the system, entropy,the free energy, etc,can be calculated by the partition function, and then macroscopic quantities of the sound field can be got by the partition function. In Hamilton system, sound propagation is studied by different model with different expressions of the quantum mechanics. Combining with group theory and the partition function,a new model is built by considering the Schrodinger equation as particle motion control equation to study sound propagation. symplectic algorithm is introduced to solve the Schrodinger equation with the complex potential. Another new model is built through the method of Feynman path integral and the partition function. The numerical simulation results show that the two model are effective in studying the propagation of acoustic waves. Hamilton Method and its Application for Aeroacoustics in this doctoral thesis paves a new way for the study of wave propagation and aeroacoustics.更多还原