A fast multipole boundary element method for three‐dimensional acoustic problems in a subsonic uniform flow,International Journal for Numerical Methods in Fluids

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A fast multipole boundary element method for three‐dimensional acoustic problems in a subsonic uniform flow
International Journal for Numerical Methods in Fluids ( IF 1.7 ) Pub Date : 2020-12-06 , DOI: 10.1002/fld.4947
Xueliang Liu _{1,

2} , Haijun Wu _{1,

2} , Weikang Jiang _{1,

2} , Ruihua Sun _{1,

2}

Affiliation

A fast multipole boundary element method (FMBEM) in a subsonic uniform flow is presented. It is based on the boundary integral equation (BIE) in a subsonic uniform flow. The convected Green's function complicates its multipole expansion as well as the implementation of the computer code. Although the Lorentz transformation allows the Helmholtz equation in the uniform flow to be reduced to the standard Helmholtz equation, the deformation of the domain complicates the boundary conditions and may cause the elements' distortion. In this work, the analytical evaluations of singular integrals are achieved. Then a nonsingular BIE in a subsonic uniform flow is obtained and is incorporated in building FMBEM with the plane wave multipole expansion of Green's function directly. Details on the implementation of the algorithm are described. Numerical examples including a pulsating sphere radiation problem, a multibody scattering problem and an aircraft model are performed to validate the accuracy and efficiency of the proposed method. Results show that FMBEM solutions are in good agreement with analytical solutions. The difference between the analytical moments and numerical moments is also investigated carefully in the implementation of the fast multipole method. Dramatical improvements on solution efficiency are observed by comparing the developed algorithm with the CBEM.

中文翻译：

亚音速均匀流中三维声学问题的快速多极边界元方法

提出了一种在亚音速均匀流中的快速多极边界元方法（FMBEM）。它基于亚音速均匀流中的边界积分方程（BIE）。所谓的格林函数使它的多极扩展以及计算机代码的实现变得复杂。尽管Lorentz变换允许将均匀流中的Helmholtz方程简化为标准Helmholtz方程，但是畴的变形使边界条件变得复杂，并可能导致元素变形。在这项工作中，实现了奇异积分的分析评估。然后得到亚音速均匀流中的非奇异BIE，并将其并入具有Green函数的平面波多极展开的FMBEM中。描述了该算法的实现细节。数值实例包括脉动球辐射问题，多体散射问题和飞机模型，以验证所提出方法的准确性和效率。结果表明，FMBEM解决方案与分析解决方案非常吻合。在快速多极子方法的实现中，还仔细研究了分析力矩和数值力矩之间的差异。通过将开发的算法与CBEM进行比较，可以观察到解决方案效率的显着提高。在快速多极子方法的实现中，还仔细研究了分析力矩和数值力矩之间的差异。通过将开发的算法与CBEM进行比较，可以观察到解决方案效率的显着提高。在快速多极子方法的实现中，还仔细研究了分析力矩和数值力矩之间的差异。通过将开发的算法与CBEM进行比较，可以观察到解决方案效率的显着提高。

更新日期：2020-12-06

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