𝔖 Bobbio Scriptorium
✦   LIBER   ✦

A Finite Element Method for Fully Nonlinear Water Waves

✍ Scribed by Xing Cai; Hans Petter Langtangen; Bjørn Fredrik Nielsen; Aslak Tveito

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
349 KB
Volume
143
Category
Article
ISSN
0021-9991

No coin nor oath required. For personal study only.

✦ Synopsis

We introduce a numerical method for fully nonlinear, three-dimensional water surface waves, described by standard potential theory. The method is based on a transformation of the dynamic water volume onto a fixed domain. Regridding at each time step is thereby avoided. The transformation introduces an elliptic boundary value problem which is solved by a preconditioned conjugate gradient method. Moreover, a simple domain imbedding precedure is introduced to solve problems with an obstacle in the water volume. Numerical experiments are presented and they show nice convergence properties of the iterative solver as well as convergence of the entire solution towards a reference solution computed by another scheme.

📜 SIMILAR VOLUMES

A finite element method for two-dimensio
A finite element method for two-dimensional water-wave problems
✍ J.W. Kim; K.J. Bai 📂 Article 📅 1999 🏛 John Wiley and Sons 🌐 English ⚖ 228 KB 👁 3 views

In this paper, the authors treat the free-surface waves generated by a moving disturbance with a constant speed in water of finite and constant depth. Specifically, the case when the disturbance is moving with the critical speed is investigated. The water is assumed inviscid and its motion irrotatio

Meshless numerical simulation for fully
Meshless numerical simulation for fully nonlinear water waves
✍ Nan-Jing Wu; Ting-Kuei Tsay; D. L. Young 📂 Article 📅 2005 🏛 John Wiley and Sons 🌐 English ⚖ 686 KB

## Abstract A meshless numerical model for nonlinear free surface water wave is presented in this paper. An approach of handling the moving free surface boundary is proposed. Using the fundamental solution of the Laplace equation as the radial basis functions and locating the source points outside

Time-accurate stabilized finite-element
Time-accurate stabilized finite-element model for weakly nonlinear and weakly dispersive water waves
✍ Zhengyong Zhong; K. H. Wang 📂 Article 📅 2008 🏛 John Wiley and Sons 🌐 English ⚖ 781 KB

## Abstract Introduction of a time‐accurate stabilized finite‐element approximation for the numerical investigation of weakly nonlinear and weakly dispersive water waves is presented in this paper. To make the time approximation match the order of accuracy of the spatial representation of the linea

Finite element beam propagation method f
Finite element beam propagation method for nonlinear optical waveguides
✍ Takashi Yasui; Masanori Koshiba; Akira Niiyama; Yasuhide Tsuji 📂 Article 📅 1999 🏛 John Wiley and Sons 🌐 English ⚖ 181 KB

A new beam propagation method based on the finite element method (FE-BPM) has been developed for the analysis of nonlinear optical waveguides. A formulation for the FE-BPM that is applicable not only to the TE mode but also to the TM mode is presented. Various techniques for enhancing the performanc