Augustus R. Okoyenta, Haijun Wu, Xueliang Liu, Weikang Jiang
{"title":"浅谈格林函数在声学问题中的应用","authors":"Augustus R. Okoyenta, Haijun Wu, Xueliang Liu, Weikang Jiang","doi":"10.1142/s2591728519500257","DOIUrl":null,"url":null,"abstract":"Green’s functions for acoustic problems is the fundamental solution to the inhomogeneous Helmholtz equation for a point source, which satisfies specific boundary conditions. It is very significant for the integral equation and also serves as the impulse response of an acoustic wave equation. They are important for acoustic problems that involve the propagation of sound from the source point to the observer position. Once the Green’s function, which satisfies the necessary boundary conditions, is obtained, the sound pressure at any point away from the source can be easily calculated by the integral equation. The major problem faced by researchers is in the process of constructing these Green’s functions which satisfy a specific boundary condition. The aim of this work is to review some of these fundamental solutions available in the literature for different boundary conditions for the ease of analyzing acoustics problems. The review covers the free-space Green’s functions for stationary source and rotational source, for both when the observer and the acoustic medium are at rest and when the medium is in uniform flow. The half-space Green’s functions are also summarized for both stationary acoustic source and moving acoustic source, derived using the image source method, equivalent source method and complex equivalent method in both time domain and frequency domain. Each of these methods used depends on the different impedance boundary conditions for which the Green’s function will satisfy. Finally, enclosed spaced Green’s functions for both rectangular duct and cylindrical duct for an infinite and finite duct is also covered in the review.","PeriodicalId":55976,"journal":{"name":"Journal of Theoretical and Computational Acoustics","volume":null,"pages":null},"PeriodicalIF":1.3000,"publicationDate":"2020-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"5","resultStr":"{\"title\":\"A Short Survey on Green’s Function for Acoustic Problems\",\"authors\":\"Augustus R. Okoyenta, Haijun Wu, Xueliang Liu, Weikang Jiang\",\"doi\":\"10.1142/s2591728519500257\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Green’s functions for acoustic problems is the fundamental solution to the inhomogeneous Helmholtz equation for a point source, which satisfies specific boundary conditions. It is very significant for the integral equation and also serves as the impulse response of an acoustic wave equation. They are important for acoustic problems that involve the propagation of sound from the source point to the observer position. Once the Green’s function, which satisfies the necessary boundary conditions, is obtained, the sound pressure at any point away from the source can be easily calculated by the integral equation. The major problem faced by researchers is in the process of constructing these Green’s functions which satisfy a specific boundary condition. The aim of this work is to review some of these fundamental solutions available in the literature for different boundary conditions for the ease of analyzing acoustics problems. The review covers the free-space Green’s functions for stationary source and rotational source, for both when the observer and the acoustic medium are at rest and when the medium is in uniform flow. The half-space Green’s functions are also summarized for both stationary acoustic source and moving acoustic source, derived using the image source method, equivalent source method and complex equivalent method in both time domain and frequency domain. Each of these methods used depends on the different impedance boundary conditions for which the Green’s function will satisfy. Finally, enclosed spaced Green’s functions for both rectangular duct and cylindrical duct for an infinite and finite duct is also covered in the review.\",\"PeriodicalId\":55976,\"journal\":{\"name\":\"Journal of Theoretical and Computational Acoustics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.3000,\"publicationDate\":\"2020-06-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"5\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Theoretical and Computational Acoustics\",\"FirstCategoryId\":\"101\",\"ListUrlMain\":\"https://doi.org/10.1142/s2591728519500257\",\"RegionNum\":3,\"RegionCategory\":\"物理与天体物理\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"ACOUSTICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Theoretical and Computational Acoustics","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.1142/s2591728519500257","RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"ACOUSTICS","Score":null,"Total":0}
A Short Survey on Green’s Function for Acoustic Problems
Green’s functions for acoustic problems is the fundamental solution to the inhomogeneous Helmholtz equation for a point source, which satisfies specific boundary conditions. It is very significant for the integral equation and also serves as the impulse response of an acoustic wave equation. They are important for acoustic problems that involve the propagation of sound from the source point to the observer position. Once the Green’s function, which satisfies the necessary boundary conditions, is obtained, the sound pressure at any point away from the source can be easily calculated by the integral equation. The major problem faced by researchers is in the process of constructing these Green’s functions which satisfy a specific boundary condition. The aim of this work is to review some of these fundamental solutions available in the literature for different boundary conditions for the ease of analyzing acoustics problems. The review covers the free-space Green’s functions for stationary source and rotational source, for both when the observer and the acoustic medium are at rest and when the medium is in uniform flow. The half-space Green’s functions are also summarized for both stationary acoustic source and moving acoustic source, derived using the image source method, equivalent source method and complex equivalent method in both time domain and frequency domain. Each of these methods used depends on the different impedance boundary conditions for which the Green’s function will satisfy. Finally, enclosed spaced Green’s functions for both rectangular duct and cylindrical duct for an infinite and finite duct is also covered in the review.
期刊介绍:
The aim of this journal is to provide an international forum for the dissemination of the state-of-the-art information in the field of Computational Acoustics.
Topics covered by this journal include research and tutorial contributions in OCEAN ACOUSTICS (a subject of active research in relation with sonar detection and the design of noiseless ships), SEISMO-ACOUSTICS (of concern to earthquake science and engineering, and also to those doing underground prospection like searching for petroleum), AEROACOUSTICS (which includes the analysis of noise created by aircraft), COMPUTATIONAL METHODS, and SUPERCOMPUTING. In addition to the traditional issues and problems in computational methods, the journal also considers theoretical research acoustics papers which lead to large-scale scientific computations.