Application of ALE to nonlinear wave radiation by a non-wall-sided structure

Abstract

Water waves generated by the forced oscillation of a 3D non-wall-sided structure are analyzed based on the fully nonlinear potential-flow theory. In order to track an exact position of the free surface, Arbitrary Lagrangian-Eulerian (ALE) scheme is used in the computation. The feature of ALE scheme is that by introducing a prescribed path (curve) for each fluid marker on the free surface, the movement of fluid marker representing the deformation of free surface is confined along a path. With properly-designed configuration of those paths, this scheme brings about several advantages compared with the Mixed Eulerian-Lagrangian scheme and the Semi-Lagrangian scheme which are extensively used. In the computation, a higher-order boundary element method (HOBEM) and the 4th-order Runge-Kutta method are adopted as the solver of an initial boundary value problem (BVP). In the validation, the radiated waves generated by a truncated circular cylinder with flare oscillating in heave or surge are studied. Regarding the calculation of hydrodynamic forces, the temporal derivative of the velocity potential (ϕt) is evaluated in an exact but simple manner, i.e. ϕt is obtained by solving a reconstructed BVP without evaluating second-order derivatives of the velocity potential. Besides hydrodynamic forces, wave profiles at specific points and wave run-ups are also computed. Comparisons of the present results against published results of corresponding computations are made. To evaluate capability of the proposed ALE scheme, bodies with curved large flare are used in the computation.