辐射声场无反射边界模拟方法的数值分析
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摘要
边界条件是声学计算的重要问题,声学计算中常用无反射边界模拟自由声场。目前无反射边界主要的模拟方法有辐射边界法、特性声阻抗法与PML法。研究无反射边界的声学数值计算,总结了三种无反射边界的理论基础,以平面波入射的自由声场为算例,对三种边界的吸声能力与应用等问题进行了分析和总结,论证了对于入射角度较大的问题,PML法具有最好的无反射能力,辐射边界法与特性声阻抗法则会产生较大的误差。
Boundary condition is an important issue in acoustic calculations, and free acoustic field is often simulated by non-reflection boundary in acoustic calculations. At present, the main simulation methods are radiation boundary method, characteristic acoustic impedance method and PML method in non-reflection boundary. Acoustic numerical calculations of non-reflection boundary were studied, the theoretical basis of three non-reflective boundaries was summarized. With plan wave incidence of free field for example, the acoustic absorption capacity and application of three kinds of boundary were analyzed and summarized. For the question of large incidence angle, PML method has the best non-reflective ability, radiation boundary method and characteristic acoustic impedance method will produce a greater error.
Boundary condition is an important issue in acoustic calculations, and free acoustic field is often simulated by non-reflection boundary in acoustic calculations. At present, the main simulation methods are radiation boundary method, characteristic acoustic impedance method and PML method in non-reflection boundary. Acoustic numerical calculations of non-reflection boundary were studied, the theoretical basis of three non-reflective boundaries was summarized. With plan wave incidence of free field for example, the acoustic absorption capacity and application of three kinds of boundary were analyzed and summarized. For the question of large incidence angle, PML method has the best non-reflective ability, radiation boundary method and characteristic acoustic impedance method will produce a greater error.
引文
[1] 孔繁敏,李康,刘新,等.波动方程FDTD算法的PML吸收边界条件的实现与验证[J]. 微波学报, 2004(01): 1-5.KONG FanMin,LI Kang,LIU Xin,et al. Implementation and validation of the PML absorbing boundary condition for wave equation FDTD method [J].Journal of Microwaves,2004(01):1-5 (In Chinese).
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[3] Xiang Xie,HaoSen Yang,Hui Zheng. A weak formulation for interior acoustic analysis of enclosures with inclined walls and impedance boundary[J]. Wave Motion,2016(65):175-186.
[4] 薛玮飞,郭金泉,陈进,等. 波叠加法在机械噪声故障特征提取中的应用研究[J]. 机械强度,2007,29(6):900-903.XUE WeiFei,GUO JinQuan,CHEN Jin,et al. Mechanical noise feature extraction based on wave superposition method[J]. Journal of Mechanical Strength,2007,29(6):900-903 (In Chinese).
[5] Villamizar V,Acosta S,Dastrup B. High order local absorbing boundary conditions for acoustic waves in terms of farfield expansions[J]. Journal of Computational Physics,2017(333):331-351.
[6] Dragonetti R,Romano R A. Errors when assuming locally reacting boundary condition in the estimation of the surface acoustic impedance[J]. Applied Acoustics,2017,115:121-130.
[7] 张洪欣,吕英华,吕剑刚.三维柱坐标系下PML的实现及近场—远场转换[J]. 哈尔滨工程大学学报,2003(05):566-570.ZHANG Hongxin,LV YingHua,LV JianGang. Application of PML in 3D cylindrical coordinates and near-field to far-field conversion[J].Journal of Harbin Engineering University,2003(05):566-570(In Chinese).
[8] 刘瑞合,印兴耀,浦义涛.波动方程模拟PML吸收影响因素分析[J]. 物探与化探,2016(04): 757-762.LIU RuiHe,YIN XingYao,PU YiTao. Analyzing PML Absorbing impact factors with wave equation simulation[J]. Geophysics & Geochemical Exploration,2016(04): 757-762(In Chinese).
[9] Birk C, Liu L,Song C. Coupled acoustic response of two-dimensional bounded and unbounded domains using doubly-asymptotic open boundaries[J]. Journal of Computational Physics,2016(310):252-284.
[10] 周凤玺,高贝贝.多孔介质瞬态分析中非分裂PML及时域有限元实现[J]. 应用数学和力学,2016, 37(2): 195-209.ZHOU FengXi,GAO BeiBei. A non-splitting PML for transient analysis of poroelastic media and its finite element implementation[J]. Applied Mathematics and Mechanics,2016,37(2):195-209(In Chinese).
[11] 邢丽.PML吸收边界条件中的角点处理方法[J]. 科学技术与工程,2011, 11(16): 3769-3771.XING Li. An effective method for handling the corner reflections for PML absorbing boundary condition[J]. Science Technology and Engineering,2011, 11(16): 3769-3771(In Chinese)
[2] 居鸿宾,沈孟育.气动声学数值模拟中无反射边界处理及声源模型的建立[J]. 上海交通大学学报, 1998(07):38-41.JU HongBin,SHEN MengYu. Non-reflection boundary conditions and sound source modeling in computational aeroacoustics [J].Journal of Shanghai Jiaotong University,1998(07):38-41(In Chinese).
[3] Xiang Xie,HaoSen Yang,Hui Zheng. A weak formulation for interior acoustic analysis of enclosures with inclined walls and impedance boundary[J]. Wave Motion,2016(65):175-186.
[4] 薛玮飞,郭金泉,陈进,等. 波叠加法在机械噪声故障特征提取中的应用研究[J]. 机械强度,2007,29(6):900-903.XUE WeiFei,GUO JinQuan,CHEN Jin,et al. Mechanical noise feature extraction based on wave superposition method[J]. Journal of Mechanical Strength,2007,29(6):900-903 (In Chinese).
[5] Villamizar V,Acosta S,Dastrup B. High order local absorbing boundary conditions for acoustic waves in terms of farfield expansions[J]. Journal of Computational Physics,2017(333):331-351.
[6] Dragonetti R,Romano R A. Errors when assuming locally reacting boundary condition in the estimation of the surface acoustic impedance[J]. Applied Acoustics,2017,115:121-130.
[7] 张洪欣,吕英华,吕剑刚.三维柱坐标系下PML的实现及近场—远场转换[J]. 哈尔滨工程大学学报,2003(05):566-570.ZHANG Hongxin,LV YingHua,LV JianGang. Application of PML in 3D cylindrical coordinates and near-field to far-field conversion[J].Journal of Harbin Engineering University,2003(05):566-570(In Chinese).
[8] 刘瑞合,印兴耀,浦义涛.波动方程模拟PML吸收影响因素分析[J]. 物探与化探,2016(04): 757-762.LIU RuiHe,YIN XingYao,PU YiTao. Analyzing PML Absorbing impact factors with wave equation simulation[J]. Geophysics & Geochemical Exploration,2016(04): 757-762(In Chinese).
[9] Birk C, Liu L,Song C. Coupled acoustic response of two-dimensional bounded and unbounded domains using doubly-asymptotic open boundaries[J]. Journal of Computational Physics,2016(310):252-284.
[10] 周凤玺,高贝贝.多孔介质瞬态分析中非分裂PML及时域有限元实现[J]. 应用数学和力学,2016, 37(2): 195-209.ZHOU FengXi,GAO BeiBei. A non-splitting PML for transient analysis of poroelastic media and its finite element implementation[J]. Applied Mathematics and Mechanics,2016,37(2):195-209(In Chinese).
[11] 邢丽.PML吸收边界条件中的角点处理方法[J]. 科学技术与工程,2011, 11(16): 3769-3771.XING Li. An effective method for handling the corner reflections for PML absorbing boundary condition[J]. Science Technology and Engineering,2011, 11(16): 3769-3771(In Chinese)