An alternative expression of the time domain free surface Green function for deep water. (1st January 2023) - Choi, Young-Myung; Bouscasse, Benjamin; Clement, Alain H.; Gentaz, Lionel; Ferrant, Pierre; Kim, Young Jun; Malenica, Sime
Abstract: An alternative expression of the time domain free surface Green's function is proposed. Its source and image source contribution satisfies the homogeneous Neumann condition on the mean free surface, therefore it can be useful for the boundary element method based on the double-body flow linearization. Furthermore, it is proved that it is also the solution of Clement's 4th order Ordinary Differential Equation (Clément, 1998). The Frobenius method with time step movement proposed by Chuang et al. (2007) is adopted for accurate and efficient evaluation. Highlights: An alternative expression of time domain free surface Green's function is provided. The source terms satisfy the homogeneous Neumann condition on the free surface. The alternative expression and its gradients satisfy Clement's 4th-order ODE. The Frobenius method is adopted to evaluate Green's function and gradients.