A panel-free method for time-domain analysis of the radiation problem

Numerical Solution of Body-Exact Problem in the Time Domain

“…Based on the work of Qiu and Hsiung (2002), the velocity potential, f(P; t), can be obtained from the desingularized integral equation in terms of source distribution as follows:…”

“…For body-exact problems, repanelization of the instantaneous wetted body surface is required at each time step. Recently, Qiu and Hsiung (2002) and Qiu et al (2004) have developed a panel-free method for the time-domain analysis. The development aimed to remove the computational errors occurred in the panel methods resulting from the geometrical approximation, the assumption of a certain degree of velocity potential or source strength distribution on a panel, and the evaluation of the singular terms in the integral equation.…”

Um método de elementos de contorno do domínio do tempo para análise de comportamento no mar de sistemas oceânicos.

“…Hess and Smith (1967) is considered a pioneering work in this topic, applying it to a wide variety of flow problems with bodies in infinite fluid. This method is by far the simplest option among other possibilities, such as the Higher Order Panel Methods which use curved panels and linear or quadratic representations of the variable quantities over surface patches (see for instance Maniar (1995) and Qiu (2001)). The use of higher order methods certainly would increase the accuracy of the solution if the number of unknowns are maintained the same, but on the other hand, the integral equations would become much more difficult to solve.…”

A higher order time domain panel method for linear and weakly non linear seakeeping problems.

“…Previous comparisons regarding computational time and accuracy for the low and higher order approaches were provided by Liu et al [1991] that applied quadratic quadrilateral elements (8 nodes) and by Maniar [1995b], who applied a B-spline description, both works dealing only with frequency domain solutions for many simulation conditions. Maniar [1995b] also adopted a Galerkin procedure to obtain a determined linear system since, usually, the number of variables are larger than equations when a single collocation point per panel is assumed . Qiu [2001] and Qiu et al [2006] presented the so-called panel free method (desingularized) for wave body interaction, with and without current, where the geometry is generically described by the coefficients of a single NURBS, as largely available in CAD packages.…”