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.

We present a comparison between two distinct numerical codes dedicated to the study of wave energy converters. Both are developed by the authors, using a boundary element method with linear triangular elements. One model applies fully nonlinear boundary conditions in a numerical wavetank environnment (and thus referred later as NWT), whereas the second relies on a weak-scatterer approach in open-domain and can be considered a weakly nonlinear potential code (referred later as WSC). For the purposes of comparison, we limit our study to the forces on a heaving submerged sphere. Additional results for more realistic problem geometries will be presented at the conference.

This paper presents the development and validation of a three-dimensional numerical wave tank devoted to studying wave-structure interaction problems. It is based on the fully nonlinear potential ow theory, here solved by a boundary element approach and using unstructured triangular meshes of the domain's boundaries. Time updating is based on a second-order explicit Taylor series expansion. The method is parallelized using the Message Passing Interface (MPI) in order to take advantage of multi-processor systems. For radiation problems, with cylindrical bodies moving in prescribed motion, the free-surface is updated with a fully Lagrangian scheme, and is able to reproduce reference results for nonlinear forces exerted on the moving body. For diraction problems, semi-Lagrangian time-updating is used, and reproduces nonlinear eects for diraction on monopiles. Finally, we study the nonlinear wave loads on a xed semi-submersible structure, thereby illustrating the possibility to apply the proposed numerical model for the design of oshore structures and oaters.

Abstract. We apply in this paper a geometrical shape optimization method for the design of the core of a SFR (Sodium-cooled Fast Reactor) in order to minimize a thermal counter-reaction known as the sodium void effect. In this kind of reactors, by increasing the temperature, the core may become liable to a strong increase of reactivity, a key-parameter governing the chain-reaction at quasi-static states. We first use the one group energy diffusion model and give the generalization to the two groups energy equation. We then give some numerical results in the case of the one group energy equation. Note that the application of our method leads to some designs whose interfaces can be parametrized by very smooth curves which can stand very far from realistic designs. We don't explain here the method that it would be possible to use for recovering an operational design but there exists several penalization methods (see [2]) that could be employed to this end.Résumé. On applique dans cet article une méthode d'optimisation géométrique dans le cadre de la conception d'un coeur de réacteur SFR (Sodium-cooled Fast Reactor, i.e. réacteurà neutron rapide refroidi au sodium) dans le but de minimiser une contre réaction thermique connue sous le nom d'effet de vidange sodium. Lorsqu'une augmentation de température survient, ce type de réacteur peutêtre sujetà une forte augmentation de réactivité, un paramètre clé dans le contrôle de la réaction en chaîne en régime quasi-statique. On a recoursà l'équation de diffusionà un groupe puis on donne la généralisation du modèle d'optimisation pour l'équation de la diffusionà deux groupes d'énergie. On présente ensuite quelques résultats numériques obtenus dans le cas de l'équationà un groupe d'énergie. On note que l'application de cette méthode conduità des designs de coeur présentant des interfaces très régulières qui sont loin d'un design de coeur faisable sur le plan technologique. A cet effet, de nombreuses méthodes de pénalisation (comme celles rencontrées dans [2]) pourraientêtre employées.

We report on the development and validation of a new Numerical Wave Tank (NWT) solving fully nonlinear potential flow (FNPF) equations, as a more efficient variation of Grilli et al.'s NWT [Grilli et al., A fully nonlinear model for three-dimensional overturning waves over arbitrary bottom, International Journal for Numerical Methods in Fluids 35 ( 2001) 829-867], which was successful at modeling many wave phenomena, including landslide-generated tsunamis, rogue waves, and the initiation of wave breaking over slopes. This earlier NWT combined a three dimensional MII (mid-interval interpolation) boundary element method (BEM) to an explicit mixed Eulerian-Lagrangian time integration. The latter was based on second-order Taylor series expansions for the mesh geometry and Dirichlet free surface boundary condition for the potential, requiring high-order derivatives to be computed in space and time. Here, to be able to solve large scale wave-structure interaction problems for surface-piercing bodies of complex geometry, of interest for ocean engineering and naval hydrodynamics applications, the NWT is reformulated to use cubic Bspline meshes and the BEM solution is accelerated with a parallelized Fast Multipole Method (FMM) based on ExaFMM, one of the fastest open source FMM to date. The NWT accuracy, convergence, and scaling are first assessed for simple cases, by comparing results with those of the earlier MII-NWT as a function of mesh size and other model parameters. The relevance of the new NWT for solving the targeted applications is then demonstrated for surface piercing fixed cylinders, for which we show that results agree well with theoretical and experimental data for wave elevation and hydrodynamic forces.