Computational Mechanics

, Volume 57, Issue 5, pp 717–732 | Cite as

Numerical modeling of undersea acoustics using a partition of unity method with plane waves enrichment

Original Paper

Abstract

A new 2D numerical model to predict the underwater acoustic propagation is obtained by exploring the potential of the Partition of Unity Method (PUM) enriched with plane waves. The aim of the work is to obtain sound pressure level distributions when multiple operational noise sources are present, in order to assess the acoustic impact over the marine fauna. The model takes advantage of the suitability of the PUM for solving the Helmholtz equation, especially for the practical case of large domains and medium frequencies. The seawater acoustic absorption and the acoustic reflectance of the sea surface and sea bottom are explicitly considered, and perfectly matched layers (PML) are placed at the lateral artificial boundaries to avoid spurious reflexions. The model includes semi-analytical integration rules which are adapted to highly oscillatory integrands with the aim of reducing the computational cost of the integration step. In addition, we develop a novel strategy to mitigate the ill-conditioning of the elemental and global system matrices. Specifically, we compute a low-rank approximation of the local space of solutions, which in turn reduces the number of degrees of freedom, the CPU time and the memory footprint. Numerical examples are presented to illustrate the capabilities of the model and to assess its accuracy.

Keywords

Underwater acoustic propagation Helmholtz equation Partition of unity method Plane waves Complex wavenumber Low-rank approximation Singular value decomposition 

Notes

Acknowledgments

This work is partially supported by KIC InnoEnergy and European Institute of Innovation and Technology (EIT) through project Offshore Test Station (OTS; 03_2011_LH03 Industry Energy Efficiency).

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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • Raúl Hospital-Bravo
    • 1
  • Josep Sarrate
    • 1
  • Pedro Díez
    • 1
  1. 1.Laboratori de Càlcul Numèric (LaCàN), Departament de Matemàtica Aplicada IIIUniversitat Politècnica de CatalunyaBarcelonaSpain

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