A fast multipole boundary element method for half-space acoustic problems in a subsonic uniform flow. (April 2022)

• Record Type: Journal Article
• Authors: Liu, Xueliang; Wu, Haijun; Sun, Ruihua; Jiang, Weikang
• Is Part Of: Engineering analysis with boundary elements. Volume 137(2022)
• Page Start: 16
• Page End: 28
• Publication Date: 2022-04
• Subjects: Boundary element method -- Half-space problems -- Subsonic uniform flow -- Fast multipole method -- Convected Green's function for half-space; Boundary element methods -- Periodicals; Engineering mathematics -- Periodicals; Équations intégrales de frontière, Méthodes des -- Périodiques; Mathématiques de l'ingénieur -- Périodiques; Boundary element methods; Engineering mathematics; Periodicals; 620.00151
• DOI: 10.1016/j.enganabound.2022.01.008
• Languages: English
• ISSNs: 0955-7997

Abstract

Abstract: This paper presents a fast multipole boundary element method (FMBEM) for half-space acoustic problems in a subsonic uniform flow. First, the fundamental solution, i.e., Green's function for half-space acoustic wave problems in a subsonic uniform flow is derived. By employing the Burton-Miller method, a convected hybrid boundary integral formula is achieved to overcome the non-uniqueness difficulty. The developed formula does not need to consider the integral on the infinite plane and it is convenient for numerical implementation. The numerical evaluation of singular integrals in the convected boundary integral formulae is also introduced. Then, the fast multipole method (FMM) for convected BEM is derived and adopted to improve the calculation efficiency and increase the computational scale. Different from the previous FMM for full-space problems, the multipole expansion and translation of the mirror-image model are the key to the FMM for half-space problems. The impact of the infinite plane on the results can be computed by building the mirror-image model. And only the structural boundary in the real domain needs to be discretized and constructed for the tree structure. Numerical examples including a pulsating half-sphere problem, a sphere model and an aircraft model in moving flows are given to validate the accuracy and efficiency of the developed method.