Wilkes Daniel R, Duncan Alec J
Centre for Marine Science and Technology, Department of Imaging and Applied Physics, Curtin University, GPO Box U1987, Perth, Western Australia 6845, Australia.
J Acoust Soc Am. 2015 Apr;137(4):2158-67. doi: 10.1121/1.4916603.
This paper presents a numerical model for the acoustic coupled fluid-structure interaction (FSI) of a submerged finite elastic body using the fast multipole boundary element method (FMBEM). The Helmholtz and elastodynamic boundary integral equations (BIEs) are, respectively, employed to model the exterior fluid and interior solid domains, and the pressure and displacement unknowns are coupled between conforming meshes at the shared boundary interface to achieve the acoustic FSI. The low frequency FMBEM is applied to both BIEs to reduce the algorithmic complexity of the iterative solution from O(N(2)) to O(N(1.5)) operations per matrix-vector product for N boundary unknowns. Numerical examples are presented to demonstrate the algorithmic and memory complexity of the method, which are shown to be in good agreement with the theoretical estimates, while the solution accuracy is comparable to that achieved by a conventional finite element-boundary element FSI model.
本文提出了一种使用快速多极边界元法（FMBEM）对水下有限弹性体的声学流固耦合（FSI）进行数值模拟的模型。分别采用亥姆霍兹方程和弹性动力学边界积分方程（BIE）对外部流体域和内部固体域进行建模，压力和位移未知量在共享边界界面处的协调网格之间进行耦合，以实现声学流固耦合。将低频快速多极边界元法应用于两个边界积分方程，将迭代解的算法复杂度从每个矩阵 - 向量乘积的O(N(2))运算降低到O(N(1.5))运算，其中N为边界未知量的数量。给出了数值算例，以证明该方法的算法和内存复杂度，结果表明与理论估计值吻合良好，同时求解精度与传统有限元 - 边界元流固耦合模型相当。
