A stabilised nodal spectral element method for fully nonlinear water waves

A Stabilised Nodal Spectral Element Method for Fully Nonlinear Water Waves

We present an arbitrary-order spectral element method for general-purpose simulation of non-overturning water waves, described by fully nonlinear potential theory. The method can be viewed as a high-order extension of the classical finite element method proposed by Cai et al (1998) [5], although the numerical implementation differs greatly. Features of the proposed spectral element method inclu...

A Finite Element Method for Fully Nonlinear Water Waves

A Finite Element Method for Fully Nonlinear Water Waves Xing Cai,∗ Hans Petter Langtangen,† Bjørn Fredrik Nielsen,∗ and Aslak Tveito∗ ∗Department of Informatics, University of Oslo, P.O. Box 1080 Blindern, N-0316, Oslo, Norway; and †Mechanics Division, Department of Mathematics, University of Oslo, P.O. Box 1053 Blindern, N-0316, Oslo, Norway E-mail: [email protected], [email protected], bjornn@i...

Quasi ALE finite element method for nonlinear water waves

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On Nonlinear Water Waves in a Channel

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

We present a numerical method for simulations of nonlinear surface water waves over variable bathymetry. It is applicable to either twoor 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 Dir...