气动声学中声传播问题的辛算法研究  

Numerical Study of Acoustic Propagation Using the Symplectic Method

作　　者：刘鑫[1] 谢军龙[1,2] 谢晴 黄河源 LIU Xin;XIE Jun-Long;XIE Qing;HUANG He-Yuan(School of Energy and Power Engineering, Huazhong University of Science ＆ Technology, Wuhan 430074, China;Green Fan Manufacturing Collaborative Innovation Center in Hubei Province, VVuhan 430074, China)

机构地区：[1]华中科技大学能源与动力工程学院,武汉430074 [2]绿色风机制造湖北省协同创新中心(培育),武汉430074

出　　处：《工程热物理学报》2018年第6期1267-1271,共5页Journal of Engineering Thermophysics

基　　金：国家自然科学基金资助项目(No.51376077)

摘　　要：引入辛算法对气动声学中的声传播问题进行了数值研究。采用Hamilton系统描述理想气体的声波方程,时间离散采用辛可分Runge-Kutta方法,空间离散采用近似解析方法,构造声波方程的保辛格式。将辛算法和有限差分算法分别在数值频散和计算效率等方面进行了对比分析,研究结果表明:辛算法能够有效地抑制数值频散,在计算效率方面具有明显的优越性。声传播特性模拟结果表明辛算法能够准确地模拟点源声辐射、声波干涉、反射及衍射现象。The numerical study of the sound propagation in air medium is carried out using the symplectic method. The acoustic wave equation is expressed in the Hamiltonian system. The secondorder Partitioned Runge-Kutta method is used for the time discretization and the nearly-analytic discrete method is used for the space discretization. Compared with the conventional finite difference scheme, the numerical dispersion and computational cost of the symplectic scheme are discussed. The results show that the symplectic method can effectively suppress the numerical dispersion and has obvious superiority in the computational efficiency. In addition, characteristics of sound propagation are simulated. It shows that the symplectic method can accurately capture the phenomena of sound radiation, interference, reflection and diffraction of sound waves.

关 键 词：数值模拟 声波方程 HAMILTON系统 辛算法 

分 类 号：O422.2[理学—声学]