Efficient calculation of the three-dimensional sound pressure field around a railway track

Preprint, 2022

The wavenumber domain Boundary Element method (or 2.5D BE) is well suited for calculating the acoustic sound field around structures with a constant cross-section along one dimension, such as noise barriers or railway tracks. By expressing the sound field along this dimension in the wavenumber domain, the numerical model is reduced from a 3D model to a 2D model at each wavenumber. A consequence of the required discrete Fourier domain representation is that the sound field is represented by periodically repeating sections, of which only one section is physically meaningful. The resolution and the number of required wavenumbers increase with this section's desired length and spatial discretization. Describing the sound field adequately to auralising the sound field without disturbing artefacts requires a large number of wavenumbers (and thus 2D BE computations), which is not feasible for large geometries.
Here, a method is introduced that allows the calculation of the 3D sound field by solving a single 2D BE problem for a dense frequency spectrum and interpolating at a higher wavenumber. The calculation efficiency is further increased by pre-calculating the acoustic transfer functions between each BE surface element and receiver positions. Combining these two methods allows the efficient calculation of the 3D sound field. The numerical approach is validated compared to a standard 2.5D BEM calculation and an analytical model. Pre-calculated transfer functions to calculate the sound radiation from railway tracks are presented and made available online.