A new ordinary differential equation for the evaluation of the frequency-domain Green function |
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| Institution: | 1. Ecole Centrale de Nantes, LHEEA Res. Dept. (ECN and CNRS) 1, rue de la Noë, 44321 Nantes, France;2. Bureau Veritas, Research Department, 92937 Paris La Défense, France;1. Faculty of Technology and Maritime Science, University of Southeast Norway, Tønsberg, Norway;2. Department of Mathematical Sciences and Technology, Norwegian University of Life Sciences, Ås, Norway;1. Deepwater Technology Research Centre (DTRC), Bureau Veritas 117674, Singapore;2. State Key Laboratory of Ocean Engineering, Collaborative Innovation Center for Advanced Ship and Deep-Sea Exploration, School of Naval Architecture, Ocean & Civil Engineering, Shanghai Jiao Tong University, Shanghai, China;1. The University Centre in Svalbard, Norway;2. Lomonosov Moscow State University, Russia;3. Zubov State Oceanographic Institute, Russia |
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| Abstract: | Clément (2013) derived a second order ordinary differential equation (ODE) satisfied by the free-surface Green function in the frequency domain. Since then, similar ODEs for the gradient of the Green function have been developed. Unfortunately, all these ODEs degenerate at zero frequency. Therefore, it is not possible to initialize the numerical solution of these ODEs from this zero frequency. Alternative methods based on the shifting of the initial condition to frequencies strictly greater than zero have then been developed.The present paper describes an alternative approach to address this issue. It involves a new function which is the solution of a modified ODE which can be solved from the zero frequency.Finally, comparisons with evaluations of the Green function using the classical direct integration method are provided. They show that the new ODE can provide accurate estimates of the Green function. |
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| Keywords: | Ordinary differential equation Green function Frequency domain Singularity |
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