Abstract
A fast computational method for fully nonlinear non-overturning water waves is
derived in two and three dimensions. A corresponding time-stepping scheme is developed
in the two-dimensional case. The essential part of the method is a fast
converging iterative solution procedure of the Laplace equation. One part of the
solution is obtained by fast Fourier transform, while another part is highly nonlinear
and consists of integrals with kernels that decay quickly in space. The number of
operations required is asymptotically O(N log N), where N is the number of nodes at
the free surface. While any accuracy of the computations is achieved by a continued
iteration of the equations, one iteration is found to be sufficient for practical computations,
while maintaining high accuracy. The resulting explicit approximation of
the scheme is tested in two versions. Simulations of nonlinear wave fields with wave
slope even up to about unity compare very well with reference computations. The
numerical scheme is formulated in such a way that aliasing terms are partially or
completely avoided.
Publisher
Cambridge University Press (CUP)
Subject
Mechanical Engineering,Mechanics of Materials,Condensed Matter Physics
Cited by
102 articles.
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