Numerical comparisons of two long-wave limit models
Stéphane Labbé; Lionel Paumond
ESAIM: Mathematical Modelling and Numerical Analysis (2010)
- Volume: 38, Issue: 3, page 419-436
- ISSN: 0764-583X
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topLabbé, Stéphane, and Paumond, Lionel. "Numerical comparisons of two long-wave limit models." ESAIM: Mathematical Modelling and Numerical Analysis 38.3 (2010): 419-436. <http://eudml.org/doc/194221>.
@article{Labbé2010,
abstract = {
The Benney-Luke equation (BL) is a model for the evolution of three-dimensional weakly nonlinear, long water waves of small amplitude. In this paper we propose a nearly conservative scheme for the numerical resolution of (BL). Moreover, it is known (Paumond, Differential Integral Equations16 (2003) 1039–1064; Pego and Quintero, Physica D132 (1999) 476–496) that (BL) is linked to the Kadomtsev-Petviashvili equation for almost one-dimensional waves propagating in one direction. We study here numerically the link between (KP) and (BL) and we point out the coupling effects emerging by considering two solitary waves propagating in two opposite directions.
},
author = {Labbé, Stéphane, Paumond, Lionel},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Benney-Luke; Kadomtsev-Petviashvili; spectral method; long wave limit.},
language = {eng},
month = {3},
number = {3},
pages = {419-436},
publisher = {EDP Sciences},
title = {Numerical comparisons of two long-wave limit models},
url = {http://eudml.org/doc/194221},
volume = {38},
year = {2010},
}
TY - JOUR
AU - Labbé, Stéphane
AU - Paumond, Lionel
TI - Numerical comparisons of two long-wave limit models
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2010/3//
PB - EDP Sciences
VL - 38
IS - 3
SP - 419
EP - 436
AB -
The Benney-Luke equation (BL) is a model for the evolution of three-dimensional weakly nonlinear, long water waves of small amplitude. In this paper we propose a nearly conservative scheme for the numerical resolution of (BL). Moreover, it is known (Paumond, Differential Integral Equations16 (2003) 1039–1064; Pego and Quintero, Physica D132 (1999) 476–496) that (BL) is linked to the Kadomtsev-Petviashvili equation for almost one-dimensional waves propagating in one direction. We study here numerically the link between (KP) and (BL) and we point out the coupling effects emerging by considering two solitary waves propagating in two opposite directions.
LA - eng
KW - Benney-Luke; Kadomtsev-Petviashvili; spectral method; long wave limit.
UR - http://eudml.org/doc/194221
ER -
References
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