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Guyenne, Philippe; Nicholls, David P.

Numerical simulation of solitary waves on plane slopes. (English) Zbl 1115.76019

Math. Comput. Simul. 69, No. 3-4, 269-281 (2005).
Summary: We present a numerical method for the computation of surface water waves over bottom topography. It is based on a series expansion representation of the Dirichlet-Neumann operator in terms of the surface and bottom variations. This method is computationally very efficient using the fast Fourier transform. As an application, we perform computations of solitary waves propagating over plane slopes and compare the results with those obtained from a boundary element method. A good agreement is found between the two methods.

Cited in 15 Documents

MSC:

76B25 Solitary waves for incompressible inviscid fluids
76M12 Finite volume methods applied to problems in fluid mechanics
65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs

Keywords:

Solitary water waves; Dirichlet-Neumann operators; Bottom topography; Geometrical perturbation methods; Boundary element method
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References:

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