A three dimensional Dirichlet-to-Neumann operator for waves over topography
Abstract
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 modeling and evolution to the two dimensional free surface. The corresponding Fourier-type 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.
Keywords
Cite
@article{arxiv.1708.00297,
title = {A three dimensional Dirichlet-to-Neumann operator for waves over topography},
author = {David Andrade and André Nachbin},
journal= {arXiv preprint arXiv:1708.00297},
year = {2018}
}