This report presents a fast multipole boundary element method (FMBEM) for acoustic problems in moving flows. The BEM offers distinct advantages for modeling acoustic propagation, including high accuracy and inherent satisfaction of the far-field radiation condition. However, significant challenges persist in solving acoustic propagation problems in moving media. This study addresses key difficulties including hypersingular integration for high-order elements in flow fields, formulation of acoustic propagation models in non-uniform flows, and fast algorithms by proposing targeted solutions. To resolve singular integrals in boundary integral equations, we develop specialized quadrature techniques for second-order curved elements in flow fields. Besides, a fast boundary integral equation theory is established for steady non-uniform potential flow. Efficient computation is enabled via multipole-transfer exponential expansions and recursive harmonic function algorithms. The resulting flow quantities serve as inputs for acoustic field calculations. Then, an acoustic propagation theory for non-uniform potential flow is formulated. Fundamental solutions for acoustic waves in non-uniform flow are derived using Taylor-Lorentz transformations and their inverses. By leveraging variable substitutions and series expansions, a fast multipole acceleration framework tailored to acoustic propagation in flows is developed. Finally, benchmark cases including flow past a sphere and pulsating sphere models are given to validate the accuracy and computational efficiency of the proposed algorithms.

Dr. Xueliang Liu received his Ph.D. degree in State Key Laboratory of Mechanical System and Vibration from Shanghai Jiaotong University in 2022. In 2023, he joined the School of Mechanical Engineering, Nanjing University of Science and Technology. His main research focuses on computational acoustics, aeroacoustics, and numerical calculation methods. His research spans the Boundary element method (BEM), Finite element method (FEM), Heterogeneous parallel computing, et al. He has led several projects and published over 10 academic papers in Applied Acoustics, Engineering Analysis with Boundary Elements, et al. Besides, he serves as a reviewer for Aerospace Science and Technology, International Journal of Computational Methods, Computer Modeling in Engineering & Sciences, et al.