Modeling underwater noise propagation: A comparative study of fully 3D Time-Domain numerical strategies

A comparative study of three numerical methods-Finite Difference (FD), Finite Volume (FV), and Spectral Element Method (SEM)-for modeling underwater acoustic propagation is presented. The time-domain acoustic wave equation is solved using an in-house FD code, the open-source SPECFEM3D software for SEM, and a newly developed FV-based acoustic solver implemented and released within the OpenFOAM framework, extending a software environment traditionally used for computational fluid dynamics to underwater acoustics applications. The methods are systematically assessed through benchmark problems, ranging from homogeneous unbounded and semi-infinite domains to the Pekeris waveguide and a Gaussian canyon. Comparisons with analytical solutions demonstrate that all solvers accurately reproduce monopole and dipole radiation in simplified configurations. However, the analysis reveals that directional sources introduce non-trivial numerical sensitivities, even in simple environments. These effects manifest as spurious reflections and dispersion-related distortions, whose severity depends on the source implementation and the numerical scheme. The results show that SPECFEM3D generally provides the highest accuracy and robustness in heterogeneous and geometrically complex environments , while the in-house FD code and FV-based solver are more sensitive to dispersion but can recover accuracy through increased spatial resolution. Strategies to mitigate source-related artifacts, such as non-reflective hard sources and reduced source regions, are discussed. A preliminary investigation of moving sources highlights their straightforward implementation in FD and FV solvers, while requiring additional care within the SPECFEM3D framework. Overall, this work provides practical guidance on the accuracy, robustness, and applicability of different solvers for simulating underwater noise in near-and far-field conditions, while laying the ground for future source-propagation coupling within acoustic analogy frameworks in OpenFOAM.