Simulation of floating structure dynamics in waves by implicit coupling of a fully non-linear potential flow model and a rigid body motion approach

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We demonstrate the accuracy and convergence of a new numerical model solving wave-structure interactions based on the fully non-linear potential flow (FNPF) theory coupled to a rigid body motion approach. This work extends an earlier model proposed by Guerber et al. (Eng Anal Bound Elements 36(7):1151–1163, 2012), restricted to fully submerged structures, by allowing to solve for freely floating bodies on the free surface. Although we are currently extending the model to three dimensions (3D), the work reported here only considers two-dimensional (2D) problems. We first introduce the FNPF model, originally developed in 2D by Grilli et al. (Eng Anal Bound Elements 6(2):97–107, 1989), Grilli and Subramanya (Comput Mech 17(6):374–391, 1996), and later extended to 3D by Grilli et al. (Int J Numer Methods Fluids 35(7):829–867, 2001). We present the implementation by Guerber et al. (Eng Anal Bound Elements 36(7):1151–1163, 2012) in the 2D-FNPF model of van Daalen’s implicit method for fluid-structure interactions [see van Daalen (Numerical and theoretical studies of water waves and floating bodies, PhD thesis, Universiteit Twente, The Netherlands 1993) and Tanizawa (Proceedings of 4th Osaka colloquium on seakeeping performance of ships 2000)]. We then detail the numerical scheme used for coupling the FNPF model to the motion of a floating rigid body. Moreover, we propose a new numerical strategy for advancing the free surface front inspired by symplectic integrators, which achieves a much better performance for energy conservation. The developed algorithm is first applied to forced motion cases, for which analytical and experimental results can be found in the literature and used as benchmarks. The accuracy of the numerical solution for the fluid and applied forces is then discussed for cases with small or large amplitude motion. In the latter case, a preliminary investigation of non-linear effects is performed for the classical application of a semi-circular heaving cylinder, by comparing the computed hydrodynamic force to the experimental measurements of Yamashita (J Soc Nav Arch 141:61–70, 1977). In particular, the comparison of the magnitude of the force harmonics, up to the third order, shows the importance of simulating non-linear interactions, which become important as the ratio of the radius of the cylinder over the wavelength increases. In a second set of applications, we assess the model accuracy in dealing with freely floating bodies. As a first test case, we consider the decaying motion of a freely heaving horizontal circular cylinder released from a non-equilibrium position above the free surface. In this more demanding computations, we verify that total energy fluid-plus-body motion is well conserved, which confirms the accuracy of the fluid-structure interaction algorithm. As a second test case, we consider the free motion of a rectangular barge in waves and compute the first-order response amplitude operators.

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Journal of Ocean Engineering and Marine Energy