scholarly journals Simulation of three‐dimensional nonlinear water waves using a pseudospectral volumetric method with an artificial boundary condition

2021 ◽  
Author(s):  
Mathias Klahn ◽  
Per A. Madsen ◽  
David R. Fuhrman
Keyword(s):  
Boundary Condition ◽  
Water Waves ◽  
Three Dimensional ◽  
Volumetric Method ◽  
Artificial Boundary ◽  
Nonlinear Water Waves ◽  
Artificial Boundary Condition

scholarly journals A D-N alternating algorithm for exterior 3-D problem with ellipsoidal artificial boundary

2021 ◽  
Vol 7 (1) ◽  
pp. 455-466
Author(s):  
Xuqiong Luo ◽  
◽  
Keyword(s):  
Boundary Condition ◽  
Convergence Analysis ◽  
Error Estimation ◽  
Harmonic Functions ◽  
Three Dimensional ◽  
Artificial Boundary ◽  
Artificial Boundary Condition ◽  
Numerical Examples ◽  
Poisson Problem ◽  
Ellipsoidal Harmonic

<abstract><p>In this study, based on a general ellipsoidal artificial boundary, we present a Dirichlet-Neumann (D-N) alternating algorithm for exterior three dimensional (3-D) Poisson problem. By using the series concerning the ellipsoidal harmonic functions, the exact artificial boundary condition is derived. The convergence analysis and the error estimation are carried out for the proposed algorithm. Finally, some numerical examples are given to show the effectiveness of this method.</p></abstract>

Nonlinear Water Waves Over a Three-Dimensional Porous Bottom Using Boussinesq-Type Model

2005 ◽  
Vol 47 (4) ◽  
pp. 231-253 ◽  
Author(s):  
Shih-Chun Hsiao ◽  
Philip L.-F. Liu ◽  
Hwung-Hweng Hwung ◽  
Seung-Buhm Woo
Keyword(s):  
Water Waves ◽  
Three Dimensional ◽  
Type Model ◽  
Nonlinear Water Waves

scholarly journals Water waves, nonlinear Schrödinger equations and their solutions

1983 ◽  
Vol 25 (1) ◽  
pp. 16-43 ◽  
Author(s):  
D. H. Peregrine
Keyword(s):  
Water Waves ◽  
Rational Solution ◽  
Three Dimensional ◽  
Length Scale ◽  
Nls Equation ◽  
Nonlinear Water Waves ◽  
Weakly Nonlinear ◽  
Nonlinear Schrödinger ◽  
Wave Induced ◽  
Modulation Length

AbstractEquations governing modulations of weakly nonlinear water waves are described. The modulations are coupled with wave-induced mean flows except in the case of water deeper than the modulation length scale. Equations suitable for water depths of the order the modulation length scale are deduced from those derived by Davey and Stewartson [5] and Dysthe [6]. A number of ases in which these equations reduce to a one dimensional nonlinear Schrödinger (NLS) equation are enumerated.Several analytical solutions of NLS equations are presented, with discussion of some of their implications for describing the propagation of water waves. Some of the solutions have not been presented in detail, or in convenient form before. One is new, a “rational” solution describing an “amplitude peak” which is isolated in space-time. Ma's [13] soli ton is particularly relevant to the recurrence of uniform wave trains in the experiment of Lake et al.[10].In further discussion it is pointed out that although water waves are unstable to three-dimensional disturbances, an effective description of weakly nonlinear two-dimensional waves would be a useful step towards describing ocean wave propagation.

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