This study deals with higher-order asymptotic equations for the water-waves problem. We considered the higher-order/extended Boussinesq equations over a flat bottom topography in the well-known long wave regime. Providing an existence and uniqueness of solution on a relevant time scale of order 1/√ε and showing that the solution’s behavior is close to the solution of the water waves equations with a better precision corresponding to initial data, the asymptotic model is well-posed in the sense of Hadamard. Then we compared several water waves solitary solutions with respect to the numerical solution of our model. At last, we solve explicitly this model and validate the results numerically.
Accepté le :
Publié le :
DOI : 10.1051/m2an/2022015
Keywords: Water waves, Boussinesq system, higher-order asymptotic model, well-posedness, traveling waves, explicit solution, numerical validation
@article{M2AN_2022__56_2_593_0,
author = {Khorbatly, Bashar and Lteif, Ralph and Israwi, Samer and Gerbi, St\'ephane},
title = {Mathematical modeling and numerical analysis for the higher order {Boussinesq} system},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
pages = {593--615},
year = {2022},
publisher = {EDP-Sciences},
volume = {56},
number = {2},
doi = {10.1051/m2an/2022015},
mrnumber = {4388379},
language = {en},
url = {https://www.numdam.org/articles/10.1051/m2an/2022015/}
}
TY - JOUR AU - Khorbatly, Bashar AU - Lteif, Ralph AU - Israwi, Samer AU - Gerbi, Stéphane TI - Mathematical modeling and numerical analysis for the higher order Boussinesq system JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2022 SP - 593 EP - 615 VL - 56 IS - 2 PB - EDP-Sciences UR - https://www.numdam.org/articles/10.1051/m2an/2022015/ DO - 10.1051/m2an/2022015 LA - en ID - M2AN_2022__56_2_593_0 ER -
%0 Journal Article %A Khorbatly, Bashar %A Lteif, Ralph %A Israwi, Samer %A Gerbi, Stéphane %T Mathematical modeling and numerical analysis for the higher order Boussinesq system %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2022 %P 593-615 %V 56 %N 2 %I EDP-Sciences %U https://www.numdam.org/articles/10.1051/m2an/2022015/ %R 10.1051/m2an/2022015 %G en %F M2AN_2022__56_2_593_0
Khorbatly, Bashar; Lteif, Ralph; Israwi, Samer; Gerbi, Stéphane. Mathematical modeling and numerical analysis for the higher order Boussinesq system. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 56 (2022) no. 2, pp. 593-615. doi: 10.1051/m2an/2022015
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