A moment-free Filon-based boundary element method for ship wave evaluation and time–frequency analysis

Abstract

To overcome challenges associated with evaluating the highly oscillatory Fourier–Kochin integrals in ship wave computations, we develop a Moment-Free Filon-type Method (MFFM). Through phase transformation, the MFFM converts kernel functions into quadratic Fourier integrals, reducing evaluation to quadratic interpolation and moment computation. Coupled with adaptive sampling, parallel acceleration on graphics processing units, and direct implementation on analytical triangular panels, the MFFM performs well throughout the computational domain and achieves high accuracy compared with the accurate Adaptive Integral Method, while remaining consistent with classical far-field asymptotic approaches, such as the Kelvin–Havelock–Peters (KHP) and Chester–Friedman–Ursell (CFU) methods. Furthermore, it exhibits advantages in accuracy and efficiency over Corrected Integral Methods based on stationary phase analysis. These advancements demonstrate that the MFFM is a unified, efficient, and high-precision numerical algorithm for ship wave calculations. Additionally, in contrast to explicit analytical source strength models based on thin-ship theory or Hogner approximations, this study obtains source distributions that strictly satisfy the three-dimensional hull boundary conditions using boundary element methods based on Neumann–Kelvin and Neumann–Michell theories. Comparative time–frequency analysis reveals that KHP calculations exhibit local wave profile and spectrogram discrepancies relative to the MFFM results, whereas CFU results show good alignment. Crucially, the BEM-derived source models reveal a distinct shift in the low-energy regions of the sliding frequency bands of diverging waves. These findings clearly underscore the necessity of utilizing high-precision wave calculation algorithms alongside rigorous hull source distributions when investigating ship wave interference patterns.