The mixed-Eulerian–Lagrangian method using high-order boundary elements, described
in Xue et al. (2001) for the simulation of fully nonlinear three-dimensional
wave–wave and wave–body interactions, is here extended and applied to the study
of two nonlinear three-dimensional wave–body problems: (a) the development of
bow waves on an advancing ship; and (b) the steep wave diffraction and nonlinear
high-harmonic loads on a surface-piercing vertical cylinder. For (a), we obtain
convergent steady-state bow wave profiles for a flared wedge, and the Wigley and
Series 60 hulls. We compare our predictions with experimental measurements and
find good agreement. It is shown that upstream influence, typically not accounted
for in quasi-two-dimensional theory, plays an important role in bow wave prediction
even for fine bows. For (b), the primary interest is in the higher-harmonic ‘ringing’
excitations observed and quantified in experiments. From simulations, we obtain fully
nonlinear steady-state force histories on the cylinder in incident Stokes waves. Fourier
analysis of such histories provides accurate predictions of harmonic loads for which
excellent comparisons to experiments are obtained even at third order. This confirms
that ‘ringing’ excitations are directly a result of nonlinear wave diffraction.
An effective analysis for three-dimensional boundary element method using analytically integrated higher-order elements.