| 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. |
