Publications
6 results found
Fabregas Flavia F, Meylan MH, 2019, An extension of general identities for 3D water-wave diffraction with application to the Diffraction Transfer Matrix, Applied Ocean Research, Vol: 84, Pages: 279-290, ISSN: 0141-1187
Interaction theories are used in numerous branches of physics to efficiently evaluate wave scattering by multiple obstacles. An example of these interaction theories is the direct matrix method introduced by Kagemoto and Yue [1], which enables fast computation of three-dimensional water-wave multiple-scattering problems. The building block of interaction theories is a mathematical operator that encapsulates the mapping between incident and scattered waves. This operator is generally referred to as T-matrix and satisfies both reciprocity and energy identities. In some branches of physics, such as acoustics and electromagnetism, these identities are well established; in hydrodynamics, however, they have only been derived for a T-matrix that maps two-dimensional incident and scattered water waves. In three dimensions, water waves can be represented as a series expansion of cylindrical eigenfunctions. In this paper, we use this representation of water waves to derive the reciprocity and energy identities satisfied by the T-matrix of the direct matrix method, known as Diffraction Transfer Matrix (dtm). The identities derived herein represent an extension of existing general relations between two diffraction solutions. We show that this extension can be applied to verify the accuracy of the dtm entries, thereby increasing the reliability of existing schemes for computing the dtm. We present results for the dtm of two geometrically different isolated obstacles, as well as for the dtm of an asymmetric array. Finally, we demonstrate that the results presented herein can be extended to floating bodies found in a wide range of ocean engineering problems.
Flavia FF, McNatt C, Rongere F, et al., 2018, A numerical tool for the frequency domain simulation of large arrays of identical floating bodies in waves, Ocean Engineering, Vol: 148, Pages: 299-311, ISSN: 0029-8018
The finite-depth interaction theory (IT) introduced by Kagemoto H. and Yue (1986) enables one to drastically speed up the computation of the added mass, damping and excitation force coefficients of a group (”farm”) of floating bodies when compared to direct calculations with standard widely available boundary element method (BEM) codes. An essential part of the theory is the calculation of two hydrodynamic operators, which characterize the way a body diffracts and radiates waves, known as Diffraction Transfer Matrix (DTM) and Radiation Characteristics (RC) respectively. Two different strategies to compute them for arbitrary geometries have been proposed in the literature (Goo, J.-S. and Yoshida, 1990; McNatt J. C. et al., 2015). The purpose of this study is to present the implementation of the former in the zeroth-order BEM solver NEMOH and to compare it with the latter by providing an insight into the DTM and the RC of a truncated vertical circular cylinder and a square box. A very good agreement between the hydrodynamic operators computed with both methodologies is obtained. In addition, hydrodynamic coefficients generated by means of the IT are verified against direct NEMOH calculations for two different array layouts. Results show the effect of hydrodynamic interactions as well as the importance of the evanescent modes truncation for closely spaced configurations.
Fabregas Flavia F, Babarit A, Clement AH, 2017, On the numerical modeling and optimization of a bottom-referenced heave-buoy array of wave energy converters, International Journal of Marine Energy, Vol: 19, Pages: 1-15, ISSN: 2214-1669
Compact arrays of small wave absorbers have been proposed as an advantageous solution for the extraction of wave energy when compared to a big isolated point absorber. Numerous challenges are associated with the numerical modeling of such devices, notably the computation of the hydrodynamic interactions among the large number of floats of which they are composed. Efficient calculation of the first-order linear hydrodynamic coefficients requires dedicated numerical tools, as their direct computation using standard boundary element method (BEM) solvers is precluded. In this paper, the Direct Matrix Method interaction theory by Kagemoto and Yue (1986) is used as an acceleration technique to evaluate the performance of a generic wave energy converter (WEC) inspired by the Wavestar SC-concept and to perform layout optimization. We show that there exists an optimum number of floats for a given device footprint. Exceeding this number results in a “saturation” of the power increase, which is undesirable for the economic viability of the device. As in previous studies on multiple absorber WECs, significant differences were observed in energy production among floats, due to hydrodynamic interactions.
Fabregas Flavia F, Clement AH, 2017, Extension of Haskind's relations to cylindrical wave fields in the context of an interaction theory, Applied Ocean Research, Vol: 66, Pages: 1-12, ISSN: 0141-1187
The Direct Matrix Method Interaction Theory (IT) proposed by Kagemoto and Yue [1] speeds up the computation of hydrodynamic coefficients for large arrays of bodies when compared to direct calculations using standard Boundary Element Method (BEM) solvers. One of the most computationally expensive parts of the matrix method is the calculation of two hydrodynamic operators, known as Diffraction Transfer Matrix (DTM) and Radiation Characteristics (RC), which describe the way an isolated geometry scatters and radiates waves, respectively. A third operator, called Force Transfer Matrix (FTM), was introduced by McNatt et al. [2] to facilitate the calculation of the forces exerted on the bodies. In this paper, a novel set of relations between the FTM and RC components is obtained using the Kochin functions specific to the cylindrical basis solutions. They extend the classical Haskind's relations, valid with incident plane waves, to the cylindrical components of the scattered and radiated fields. Moreover, an alternative demonstration of the identities is given, which does not rely on the far-field asymptotic representation of the potential. Additional expressions are provided that relate the hydrodynamic coefficients and the RC for isolated bodies as well as for arrays, and numerical checking of the derived mathematical expressions is presented. These new relations can be used to speed up calculation of the hydrodynamic operators required for the use of the IT and to test its accuracy.
Fabregas Flavia F, 2016, Computation of the diffraction transfer matrix and the radiation characteristics in the open-source BEM code NEMOH, Proceedings of the ASME 2016 35th International Conference on Ocean, Offshore and Arctic Engineering
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