Numerical modeling of the underwater acoustic impact of offshore stations

• Autores: Raúl Hospital Bravo
• Directores de la Tesis: José Sarrate Ramos (dir. tes.) , Pedro Díez Mejía (codir. tes.)
• Lectura: En la Universitat Politècnica de Catalunya (UPC) ( España ) en 2021
• Idioma: español
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• Resumen

  • The design of offshore power stations (for wind, wave or tidal energy generation) requires assessing their environmental impact. In particular, it is of the major importance to predict the impact of the generated subsea noise on the marine fauna, especially sea mammals and fishes. Here, the noise propagation is modelled with the Helmholtz equation and numerically solved using a Partition of Unity Method (PUM). The aim is simulating the underwater sound propagation of multiple non-impulsive sources. The output of the simulations consists of spatial distributions of the sound pressure level.

    The mathematical model at hand considers the most relevant aspects involved in environmental underwater acoustics. Specifically, Helmholtz equation allows accounting for the most important wave phenomena: absorption, interference, reflection, refraction and diffraction. For instance, the acoustic absorption produced by seawater is represented by the imaginary part of the wavenumber. In addition, a non-uniform wavenumber that depends on the salinity, temperature and depth is considered. The model is completed with a set of boundary conditions providing a specific treatment for the reflective properties of the sea bottom and surface. The input noise is also introduced as a boundary condition. Finally, Perfectly Matched Layers (PMLs) are placed at the lateral artificial boundaries of the domain to avoid spurious reflections.

    The numerical strategy is based on a PUM enriched with plane waves. The plane wave functions are combined with the classical polynomial shape functions (hat functions, a partition of unity preserving the continuity of the approximation space among elements). The choice of plane waves provides two main advantages. On the one hand, since the enriching functions satisfy the governing equation and include a priori knowledge of the solution, they mitigate the pollution error that is intrinsic to the solutions obtained with standard polynomial approximations. On the other hand, they allow using coarser meshes with a larger element size. This leads to a drastic reduction in the number of degrees of freedom. Therefore, the method is well suited for solving the Helmholtz equation in large domains (from hundreds of meters to kilometers) compared to the characteristic wavelength (from centimeters to meters).

    However, since the plane waves are described by complex exponential functions, the computation of the elemental matrices entails the integral of highly-oscillatory functions. This increases the requirements involved in the integration step and makes the standard Gauss-Legendre rules lose their competitiveness. In the 2D version of the tool, we overcome this drawback by implementing an existing semi-analytical rule. In the 3D version, we develop a novel efficient rule to integrate highly oscillatory functions over tetrahedra. The integrand is expressed as the product of a non-oscillatory part and a complex exponential function. The rule is designed to be exact, except round-off errors, for integrals with a polynomial non-oscillatory part, which is the case of the Helmholtz equation solved with the PUM enriched with plane waves.

    To conclude, we present several examples that assess and illustrate the capabilities of the tool, including sea water absorption, homogeneous or heterogeneous media, seabeds with non-uniform transmission coefficient, and single or multiple sources.