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

Abstract

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, 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][62][63][64][65][66][67][68][69][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.

Fully Nonlinear Potential Flow Simulations of Wave Shoaling Over Slopes: Spilling Breaker Model and Integral Wave Properties

“…Such numerical solutions have been shown to agree very well with laboratory experiments, for nonlinear waves propagating up to the breaking point (including wave overturning for Lagrangian models) in deep water or over constant depth, e.g., [5,22,26], and over a varying nearshore bathymetry and topography, e.g., [33,37,44,46,47,55,65,85,88,103]. Similar models have also been used to simulate nonlinear wave interactions with fixed or floating/advancing structure, e.g., [20,48,50,51,57,78,101]. Reviews of such models to date can be found in [32,42].…”

“…In these so-called numerical wave tanks (NWTs; a termed coined by [39]), waves can be generated by internal sources, wavemakers, or other analytical/numerical solutions, e.g., [23,35,37,[42][43][44]46,47,82]. After propagating over an arbitrary bottom and possibly interacting with moving/fixed structures/bodies, e.g., [20,48,51,101], waves are then dissipated in absorbing beaches and/or using actively absorbing boundaries [11][12][13]23,25,26,[35][36][37]48].…”

A 3d Isogeometrical Boundary Element Analysis for Non-Linear Gravity Wave Propagation

“…Here, we use an auxiliary BIE to find a more accurate approach. As proposed by Dombre et al [3,33], an analogous BIE for ψ = ∂φ/∂t can be considered. This auxiliary BIE does not increase significantly the computational cost because the discretization is the same as in the main BIE.…”

“…More recently, Hannan et al [31,32] studied the interactions between water waves and fully submerged fixed or moving structures. In the same line, but limited to 2D, Dombre et al [33] extended the early work presented in [34] to study the dynamics of free fully submerged structures.…”

Time-domain simulation of large-amplitude wave–structure interactions by a 3D numerical tank approach

“…Many improved numerical schemes have been devised to handle this coupling, e.g. the acceleration potential method of Tanizawa (1995Tanizawa ( , 1996, the implicit coupled scheme of Dombre et al (2015).…”