Article information

1998 , Volume 3, ¹ 3, p.55-71

Protopopov B.E.

An efficient numerical method for calculation of strongly nonlinear water waves

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.

[full text] Classificator Msc2000:
*76B15 Water waves, gravity waves; dispersion and scattering, nonlinear interaction
76M20 Finite difference methods

Keywords: Crank-Nicholson scheme, elliptic problem, stabilizing corrector scheme, equation of divergent type, breaking waves, overturning waves, mixed Eulerian-lagrangian formulation, Lagrangian coordinates

Author(s):
Protopopov Boris Egorovich
PhD.
Position: Research Scientist
Office: Lavrentyev Institute of Hydrodynamics
Address: 630090, Russia, Novosibirsk
Phone Office: (383) 333 29 36
E-mail: boris@hydro.nsc.ru


Bibliography link:
Protopopov B.E. An efficient numerical method for calculation of strongly nonlinear water waves // Computational technologies. 1998. V. 3. ¹ 3. P. 55-71
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