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A three-dimensional Dirichlet-to-Neumann operator for water waves over topography

  • D. Andrade (a1) and A. Nachbin (a1)


Surface water waves are considered propagating over highly variable non-smooth topographies. For this three-dimensional problem a Dirichlet-to-Neumann (DtN) operator is constructed reducing the numerical modelling and evolution to the two-dimensional free surface. The corresponding discrete Fourier integral operator is defined through a matrix decomposition. The topographic component of the decomposition requires special care, and a Galerkin method is provided accordingly. One-dimensional numerical simulations, along the free surface, validate the DtN formulation in the presence of a large-amplitude rapidly varying topography. An alternative conformal-mapping-based method is used for benchmarking. A two-dimensional simulation in the presence of a Luneburg lens (a particular submerged mound) illustrates the accurate performance of the three-dimensional DtN operator.


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Andrade and Nachbin supplementary movie
Focusing by the Luneburg lens: evolution and refraction of the velocity potential by the submerged circular mound.

 Video (7.1 MB)
7.1 MB

A three-dimensional Dirichlet-to-Neumann operator for water waves over topography

  • D. Andrade (a1) and A. Nachbin (a1)


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