Daniel R. Wilkes

Acoustic coupled fluid–structure interactions using a unified fast multipole boundary element method

This paper presents a numerical model for the acoustic coupled fluid-structure interaction (FSI) of a submerged finite elastic body using the fast multipole boundary element method (FMBEM). The Helmholtz and elastodynamic boundary integral equations (BIEs) are, respectively, employed to model the exterior fluid and interior solid domains, and the pressure and displacement unknowns are coupled between conforming meshes at the shared boundary interface to achieve the acoustic FSI. The low frequency FMBEM is applied to both BIEs to reduce the algorithmic complexity of the iterative solution from O(N(2)) to O(N(1.5)) operations per matrix-vector product for N boundary unknowns. Numerical examples are presented to demonstrate the algorithmic and memory complexity of the method, which are shown to be in good agreement with the theoretical estimates, while the solution accuracy is comparable to that achieved by a conventional finite element-boundary element FSI model.

COMPILE—A Generic Benchmark Case for Predictions of Marine Pile-Driving Noise

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.

Numerical Modeling of Radiated Sound for Impact Pile Driving in Offshore Environments

In this paper, a coupled near-to-far-field numerical model for predicting the acoustic emissions from impact pile driving in offshore environments is presented. The near-field region of the pile is modeled via an axisymmetric finite element method (FEM) model which is solved in the frequency domain. The calculated radiated field at a chosen radial distance in the FEM model is then expanded into a series of local normal modes (NMs) which are propagated into the far field, to predict the piling sound characteristics, such as the peak pressure and sound exposure levels, at large ranges. Numerical examples are presented for the same pile configuration adopted for the COMPILE 2014 benchmark workshop on predicting offshore pile-driving noise, and these results are compared in both the near and far fields to those of several other research groups who presented results at the workshop. Results from the present FEM-NM near-to-far-field model are shown to be generally in good agreement with those results from the other research groups. In the near field, similar signal waveforms are predicted by the various models which employ the same pile wall boundary conditions. In the far field, the selected models showed a variation of ±1 dB at 1.5 km, and ±4 dB at 50 km for the predicted peak pressure levels, and a variation of ±1.5 dB over the 50-km range for the predicted sound exposure levels.

Non-negative intensity for coupled fluid–structure interaction problems using the fast multipole method

The non-negative intensity (NNI) method is applied to large-scale coupled fluid-structure interaction (FSI) problems using the fast multipole boundary element method (FMBEM). The NNI provides a field on the radiating structure surface that consists of positive-only contributions to the radiated sound power, thus avoiding the near-field cancellation effects that otherwise occur with the sound intensity field. Thus far the NNI has been implemented with the boundary element method (BEM) for relatively small problem sizes to allow for the full BEM coefficient and inverse matrices to be explicitly constructed and stored. In this work, the FMBEM is adapted to the NNI by calculating the eigenvalue solution of the symmetric acoustic impedance matrix using the FMBEM via a two-stage solution method. The FMBEM implementation of the NNI is demonstrated for a large-scale model of a submerged cylindrical shell. The coupled FSI problem is first solved using a finite element-FMBEM model and the resulting surface fields are then used in the FMBEM calculation of the NNI. An equivalent reactive NNI field representing the evanescent near-field radiation is demonstrated and the effect of the chosen number eigenvectors on the NNI field is investigated.

Sound radiation from impact-driven raked piles

Sound emissions from impact pile driving of raked piles present a significant azimuthal dependence in the radiated sound field due to the non-axisymmetric orientation of the pile. In this work the sound radiation from raked piles is modeled using a finite element method (FEM) model of the pile and near-field region. The near-field model of the sound field is then used as input into a normal mode model to predict the sound radiation in the far-field. The azimuthal dependence of the radiated sound field is shown to be accurately predicted using an equivalent axisymmetric FEM model of the pile configuration, thus negating the need to construct a fully three-dimensional model (3D) of the raked pile. This is achieved by matching the radiated field from the equivalent axisymmetric pile model to a vertical array of phased point sources, and then horizontally offsetting the source locations to match the incline of the raked pile. The resulting sound field closely matches the numerical predictions from a fully 3D FEM model of the raked pile. The results of numerical modeling are compared to corresponding acoustic measurements taken on the North West shelf of Western Australia.

Numerical Modelling of Sound Radiation from Marine Pile Driving over Elastic Seabeds

This work investigates the underwater sound emission of marine pile driving over elastic seabeds. The finite element method is used to model sound pressure in the near field of an axisymmetric pile and environment model, where the seabed is modelled as both fluid (fluid sand) and elastic (sand, calcarenite) materials. The presented results show that the inclusion of shear in the seabed has a marked effect on the characteristics of the radiated acoustic field in the water column, even for seabed materials which have a low shear speed. In particular, the secondary structural waves reflected from the pile ends in the elastic seabed model emit significantly less acoustic energy compared to the fluid seabed models. Scholte waves also can be observed to propagate along the fluid–solid interface in the elastic seabed models.

Application of the fast multipole boundary element method to underwater acoustic scattering.

Abstract A numerical model is being developed in the MATLAB programming environment to model the acoustic field scattered from a submarine hull. Due to the acoustic impedance properties of water, small particle velocities yield large acoustic pressures, resulting in coupled fluid-structure interactions. Numerical methods can be employed to calculate the scattered acoustic field for complex geometries. Traditionally, these techniques required both significant memory and computational time, limiting their usefulness. Recently, the fast multipole algorithm (FMA) has been used to efficiently calculate the acoustic field on an object’s surface, while the finite element method was used to model the object’s interior. The pressure hull of a submarine can be represented as a piecewise continuous isotropic elastic solid, thus the FMA can also model the submarine interior, with the unknowns expressed on each surface. A possible method for coupling an exterior acoustic model to a structural model, both calculated via the FMA, is outlined here. Some initial acoustic fast multipole boundary element method results are presented.