A self-developed code based on the BEM for the determination of the backscattered sound pressure level in the far field was extended so that additional FEM shell elements and thus elastic material properties can be considered. For this purpose, a separate FEM equation system is built up and directly integrated into the system of the BEM via corresponding transformation matrices. A common variant for solving the FEM-specific parts is to use a solver based on eigenvalue calculations, which provides the corresponding eigenfrequencies and eigenvectors of the uncoupled FEM equation system for a given upper cutoff frequency. It can be observed that only a part of the determined modes has a considerable sound radiation efficiency and is therefore relevant for the result. An algorithm determines these modes by a fast post-processing routine considering a given percentage, reduces the size of the eigenvalue equation system accordingly, and thus shortens the solution time. Furthermore, it was investigated whether the condition of the entire system of equations is improved by removing the irrelevant modes when using iterative solution methods and whether the number of iterations can thus be reduced. The paper describes the basics of FEM coupling with BEM, presents the reduction algorithm used and shows the results obtained for corresponding test structures depending on the reduction percentage used.

While it is straightforward to include the beam pattern of a sonar in ray models and normal mode models, things become more challenging for parabolic equation models. Two methods are compared in this paper. The first method uses an array starter for the parabolic equation model, derived by MacGillivray and Chapman as a generalization of Collins’ self-starter for a point source. Range propagation of the depth-dependent pressure field generated by this array starter then contains the effects of the beam pattern of the respective array. The second method inverts the computation direction so that the beam pattern can be applied to the simulation result for the complex sound pressure. This is done by performing a windowed Fourier transform into vertical wavenumber space at the sonar depth, thereby decomposing the sound pressure field into propagation angles allowing for multiplication with the beam pattern. This method is not limited to parabolic equation models. Both methods have been realized for WTD 71’s parabolic equation code PESSim (Parabolic Equation Sound Simulation). Using a homogeneous half-space with an analytic reference solution, the two methods are validated and compared. Both methods perform well while each has its advantages and disadvantages.

The prediction of underwater noise emissions from impact pile driving during near-shore and offshore construction activities and its potential effect on the marine environment has been a major field of research for several years. A number of different modeling approaches have been suggested recently to predict the radiated sound pressure at different distances and depths from a driven pile. As there are no closed-form analytical solutions for this complex class of problems and for a lack of publicly available measurement data, the need for a benchmark case arises to compare the different approaches. Such a benchmark case was set up by the Institute of Modelling and Computation, Hamburg University of Technology (Hamburg, Germany) and the Organisation for Applied Scientific Research (TNO, The Hague, The Netherlands). Research groups from all over the world, who are involved in modeling sound emissions from offshore pile driving, were invited to contribute to the first so-called COMPILE (a portmanteau combining computation, comparison, and pile) workshop in Hamburg in June 2014. In this paper, the benchmark case is presented, alongside an overview of the seven models and the associated results contributed by the research groups from six different countries. The modeling results from the workshop are discussed, exhibiting a remarkable consistency in the provided levels out to several tens of kilometers. Additionally, possible future benchmark case extensions are proposed.

The acoustic wave propagator (AWP) is the application of the time evolution operator on the acoustic wave equation for stationary systems in a polynomial expansion of Chebychev polynomials. It allows to increase the time step by more than one order of magnitude compared to finite difference time domain (FDTD) codes. In contrast to other implementations of the AWP the spatial differentiation is carried out with finite difference techniques because this allows the use of the perfectly matched layer formulation as absorbing boundary conditions. The formulation includes the direct implementation of acoustic sources with sinusoidal time evolution. Other sources can be synthesized by their Fourier components. For the calculation of large areas the explicit formulation of a large system matrix can be avoided by calculating the propagation equations for each time step at row and column level repeatedly which reduces memory requirements notably. This procedure and the suitability of the finite difference approach for parallelization makes the extension to fully three dimensional calculations possible. Examples for benchmark problems with sound propagation in air and water are given.

Different numerical approaches for the physical phenomena of scattering waves from an obstacle are presented. They are based on different integral formulations. Fluid structure interaction effects are numerically treatable as well. We use the Boundary Element Method (BEM) in different approaches because the inherently satisfied Sommerfeld radiation condition makes sure that no reflecting waves from boundaries at infinity occur. One of the biggest disadvantages of numerical methods like BEM is the fact that they have difficulties with handling the high frequency range. For the high frequency range approximations like the Kirchhoff–Helmholtz integral equation have to be used. With varying assumptions of the reflecting behavior of the structure different approaches for the higher frequency range are obtained, where the explicit solving of a system of equations is not necessary. Another high frequency approach is the plane wave approximation which is compared with the Kirchhoff approach of the first kind. Additionally a modified Kirchhoff approach is introduced. Because the incident pressure on the scatterer's surface is known the integral is evaluated analytically on triangular patches. The discretization is no longer frequency dependent and the size of the patches only depends on the curvature of the structure. Large planar parts can be discretized with one element only. This leads to a substantial advantage in terms of calculation time over the traditional Kirchhoff approach. Like the traditional approach this procedure is valid under the assumption of high frequency or far field conditions.