Comparison of existing methods for the calculation of the infinite water depth free-surface Green function for the wave-structure interaction problem

In this study, the mathematical expressions and numerical methods for the free-surface Green function of the linearized wave-structure problem in deep water and in the frequency domain are investigated. Twelve different expressions are reviewed and analyzed. All these expressions are exact mathematical solutions for the propagation of waves from a pulsating source located in the fluid domain. However, their numerical evaluation is challenging. Dedicated numerical methods have been developed. They include series expansions, polynomials, table interpolations, multipole expansions, approximations with elementary functions, etc. In this work, four methods were implemented: the Newman's method [1], the Delhommeau's method [2], the Telste-Noblesse's method [3] and the Wu et al.'s method [4]. Their CPU time and accuracy are compared. It is found that the average computational time for Newman's method is 5.745 x 10(-7). It is 5.782 x 10(-8) for the Delhommeau's method. For Telste-Noblesse's method and Wu et al.'s methods, they are 4.642 x 10(-8) and 1.491 x 10(-9), respectively. The accuracy is respectively 6D(6 decimals), 5D and 3D for the Newman's method, the Telste-Noblesse's method and the Wu et al.'s method. For the Delhommeau's method, it is 3D except when the vertical coordinate is close to 0. The accuracy of the Delhommeau's method can be increased significantly by refining the discretization of the space variables for the tabulated functions and by using higher interpolation methods, at cost of increased computational time.