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.
Dealing with freely-floating bodies in the framework of non-linear potential flow theory may require solving Laplace's equation for the time derivative of the velocity potential. At present, there are two competing formulations for the body boundary condition. The first one was derived by Cointe [Cointe(1989)] in 2D. It was later extended to 3D by van Daalen [van Daalen(1993)]. The second formulation was derived by Tanizawa [Tanizawa(1995)] in 2D. It was extended to 3D by Berkvens [Berkvens(1998)]. In this paper, a proof is given that the Cointe-Van Daalen's and the Tanizawa-Berkvens' formulations are equivalent. It leads to a simplified version of Cointe-Van Daalen's formulation. The formulation is validated against the analytical solution for a moving sphere in an unbounded water domain.
In continuation of [1], this paper presents the progress made towards the development of a new modeling tool based on the Weak-Scatterer approaches. Recent developments are the coupling of the fluid and body solver in order to predict the free motion response of the body. Pressure field over the wetted area is obtained by solving an additional boundary value problem for the time derivative of the velocity potential. Tanizawa’s [2] and Cointe’s [3] formulations for the acceleration condition on the body are revisited. Numerical prediction with the present method for a submerged body in vertical free motion is presented and energy conservation is verified. In order to adapt the mesh to the moving body geometry, advanced mesh moving schemes have been integrated based on radial basis functions [4] and spring analogy methods. In this way it is possible to solve the problem with an Arbitrary Euler Lagrangian formalism and preserve the order of the numerical scheme. However moving mesh methods are limited in time and automatic remeshing generation algorithms have been integrated in order to enable simulating longer durations. Finally, comparisons of wave diffraction and radiation predicted by linear theory, a fully nonlinear BEM solver and the present method are shown.
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