A Time-Domain Wavenumber Integration Model for Underwater Acoustics Based on the High-Order Finite Difference Method

Abstract

Simulating the acoustic field excited by pulse sound sources holds significant practical value in computational ocean acoustics. Two primary methods exist for modeling underwater acoustic propagation in the time domain: the Fourier synthesis technique based on frequency decomposition and the time-domain underwater acoustic propagation model (TD-UAPM). TD-UAPMs solve the wave equation in the time domain without requiring frequency decomposition, providing a more intuitive explanation of the physical process of sound energy propagation over time. However, time-stepping numerical methods can accumulate numerical errors, making it crucial to improve the algorithm’s accuracy for TD-UAPMs. Herein, the time-domain wavenumber integration model SPARC was improved by replacing the second-order finite element method (FEM) with the high-order accuracy finite difference method (FDM). Furthermore, the matched interface and boundary (MIB) method was used to process the seabed more accurately. The improved model was validated using three classic underwater acoustic benchmarks. By comparing the acoustic solutions obtained using the FDM and the FEM, it is evident that the improved model requires fewer grid points while maintaining the same level of accuracy, leading to lower computational costs and faster processing compared to the original model.

Keywords

• wave equation
• underwater acoustic propagation
• depth-separated wave equation
• matched interface and boundary method (MIB)