A High-Order Spectral Method for Nonlinear Water Waves over Moving Bottom Topography

Philippe Guyenne, David P. Nicholls
2008 SIAM Journal on Scientific Computing  
We present a numerical method for simulations of nonlinear surface water waves over variable bathymetry. It is applicable to either two-or three-dimensional flows, as well as to either static or moving bottom topography. The method is based on the reduction of the problem to a lower-dimensional Hamiltonian system involving boundary quantities alone. A key component of this formulation is the Dirichlet-Neumann operator which, in light of its joint analyticity properties with respect to surface
more » ... espect to surface and bottom deformations, is computed using its Taylor series representation. We present new, stabilized forms for the Taylor terms, each of which is efficiently computed by a pseudospectral method using the fast Fourier transform. Physically relevant applications are displayed to illustrate the performance of the method; comparisons with analytical solutions and laboratory experiments are provided.
doi:10.1137/060666214 fatcat:2nw2qugegvfxbk6yyywnrhq3my