1998 , Volume 3, № 3, p.55-71

An efficient numerical method for the calculation of strongly nonlinear water waves, including overturning ones, is developed. The method is based on the mixed Eulerian-Lagrangian formulation. The basic idea of this formulation is extended to the entire fluid domain. It implies that, not nly free-surface but also rigid-boundary and interior nodes of a computational grid are moved as fluid particles. This makes water motion more visual, as well as makes it possible to generate a computational grid only once and thus to save the CPU time and memory. One more distinctive feature of the present numerical method is space discretization with the help of splines: derivatives of any function are evaluated analytically, by differentiating the spline which approximates this function. The numerical method is tested by three problems: on a liquid ellipse, on an overturning bore and on a disturbed solitary wave of large amplitude. The results of test calculations demonstrate high accuracy and wide capability of the method developed.

*76B15 Water waves, gravity waves; dispersion and scattering, nonlinear interaction

76M20 Finite difference methods