A note on the relative efficiency of methods for computing the transient free-surface Green function. (1st July 2016)

• Record Type: Journal Article
• Authors: Bingham, Harry B.
• Is Part Of: Ocean engineering. Volume 120(2016)
• Page Start: 15
• Page End: 20
• Publication Date: 2016-07-01
• Subjects: Time-domain Green function -- Integration of ODEs -- Wave–structure interaction -- Marine hydrodynamics; Ocean engineering -- Periodicals; Ocean engineering; Periodicals; 620.4162
• DOI: 10.1016/j.oceaneng.2016.05.020
• Languages: English
• ISSNs: 0029-8018

Abstract

Abstract: A number of papers have appeared recently on computing the time-domain, free-surface Green function. Two papers in particular, Chuang et al. (2007) andLi et al. (2015) considered the method developed byClement (1998) who showed that this Green function is the solution to a fourth-order Ordinary Differential Equation (ODE). This ODE has been suggested as a means for speeding up the calculation of the Green function coefficients compared to the standard algorithms developed for example byNewman (1992) . Clement solved the ODE using the classical fourth-order, four-step Runge–Kutta scheme (RK44) with a fixed time step size. The two papers mentioned above proposed alternative numerical methods which are claimed to be more efficient. In this note we consider the relative efficiency of these four methods on a representative test case, and conclude that the standard method is the most efficient. Of the ODE-based methods, the method ofChuang et al. (2007) is found to be slightly more efficient than the RK44 method, while the method ofLi et al. (2015) is at least an order of magnitude less efficient. It is also pointed out that ODE methods have yet to be extended to include finite water depth. Abstract : Highlights: The standard method is found to be more efficient than ODE-based methods. Of the ODE methods, Chuang et al. (2007) and RK44 are faster thanLi et al. (2015) . The standard method also includes the effects of finite water depth.