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.