Nonlinear time domain analysis of vertical ship motions

An Evaluation of Wave Energy Generation and Cost of Energy in the Black Sea

“…The heave displacement of the float of an axisymmetric WEC is computed by solving the equation given in Eq. ( 10) in the time domain (Bruzzone & Grasso, 2007). This equation is solved by employing 4 th order Runge-Kutta method and a family of Runge-Kutta-Nyström methods with 5 th , 6 th , and 7 th orders of accuracy (Fehlberg, 1974).…”

Nonlinear effects on motions and loads using an iterative time-frequency solver

“…Different methods in the frequency domain could in principle be chosen to evaluate the quantities necessary for the procedure indicated in the previous paragraph as, for instance, a strip theory, a Rankine source method (Bruzzone and Grasso, 2007) or a 3D theory based on Green functions.…”

Exact pressure integrations on submerged bodies in waves using a quadtree adaptive mesh algorithm

“…In (13), and elsewhere, terms such as ΔC are to be understood as in ΔΘ = Θ(1) À Θ(0), where Θ may represent any of the functions defined in (8)(9)(10). ;…”

“…In light of this, this paper concerns the development of a fast, simple, easy to implement and sufficiently accurate methodology of mesh adaptation and pressures integration. The works in are good examples of instantaneous wet surface consideration, using a panel method (2D mesh); comparisons between methods using several nonlinear approaches—including of the type described here—may be found in .…”

“…In light of this, this paper concerns the development of a fast, simple, easy to implement and sufficiently accurate methodology of mesh adaptation and pressures integration. The works in [8][9][10] are good examples of instantaneous wet surface consideration, using a panel method (2D mesh); comparisons between methods using several nonlinear approaches-including of the type described here-may be found in [11][12][13][14][15].In order to avoid the necessity of refinement of the mesh due to significant intra-element gradients of the pressures, element-wise exact analytical formulations for hydrostatic and full Froude-Krylov forces calculation are derived and implemented; linear gravity waves are considered.Given that traditional, naval architecture, hydrostatic analyses are performed by integrating areas of sequential strips that discretize the hulls, computing pressures on mesh elements, as opposed to areas on strips, with the same objective (which was the case of its first applications) came out to be named pressure integration techniques. Quantities such as immersed volumes are, therefore, the result of direct pressure integration on the wet surfaces, which allows for easier consideration of complex geometries.…”