Efficient Taylor-expansion reformulation of the 3D High-Order Spectral Numerical Wave Tank

This work presents a Taylor-expansion-based reformulation of the classical HOS-NWT (High-Order Spectral Numerical Wave Tank) aimed at significantly reducing its computational complexity in three dimensions. The proposed approach reduces the dominant computational cost from 𝒪 ⁡ ( 𝑁 𝑥 ⁢ 𝑁 2 𝑦 ⁢ 𝑁 𝑧 ) to 𝒪 ⁡ ( 𝑁 𝑥 ⁢ 𝑁 𝑦 ⁢ 𝑀 T E ⁢ ( 𝑁 𝑧 + l o g ⁡ 𝑁 𝑦 + 1 ) ) , where 𝑀 T E denotes the Taylor expansion order. The reformulation preserves the spectral representation of the original solver while decomposing the coupled boundary-fitted evaluations through Taylor expansion, thereby enabling efficient implementation using the fast discrete cosine transform. Theoretical analyses and numerical experiments confirm the convergence and accuracy of the method, demonstrating substantial performance improvements. The proposed approach is further validated against laboratory measurements in strongly nonlinear short-crested seas, including directional frequency-focused wave groups (close to breaking) and long-term irregular wave conditions with large directional spreading. For the near-breaking directional frequency-focused wave case, a speed-up factor of approximately four is achieved with respect to the original HOS-NWT. The results show that the reformulation accurately and efficiently simulates strongly nonlinear wave generation and propagation in complex short-crested sea states.