Year: 2018
Communications in Computational Physics, Vol. 23 (2018), Iss. 1 : pp. 1–29
Abstract
In this paper we review the history and current state-of-the-art in modelling of long nonlinear dispersive waves. For the sake of conciseness of this review we omit the unidirectional models and focus especially on some classical and improved BOUSSINESQ-type and SERRE–GREEN–NAGHDI equations. Finally, we propose also a unified modelling framework which incorporates several well-known and some less known dispersive wave models. The present manuscript is the first part of a series of two papers. The second part will be devoted to the numerical discretization of a practically important model on moving adaptive grids.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cicp.OA-2016-0179a
Communications in Computational Physics, Vol. 23 (2018), Iss. 1 : pp. 1–29
Published online: 2018-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 29
Keywords: Long wave approximation nonlinear dispersive waves shallow water equations solitary waves.
-
The Use of the NAMI-DANCE Computational Complex on the Problem of Tsunami Waves
Zaytsev, A. I. | Kurkin, A. A. | Pelinovsky, E. N. | Yalçıner, A.Journal of Applied Mechanics and Technical Physics, Vol. 61 (2020), Iss. 7 P.1140
https://doi.org/10.1134/S0021894420070214 [Citations: 1] -
The one-dimensional Green–Naghdi equations with a time dependent bottom topography and their conservation laws
Kaptsov, E. I. | Meleshko, S. V. | Samatova, N. F.Physics of Fluids, Vol. 32 (2020), Iss. 12
https://doi.org/10.1063/5.0031238 [Citations: 6] -
Tsunami Inundation Modelling in a Built-In Coastal Environment with Adaptive Mesh Refinement: The Onagawa Benchmark Test
Aljber, Morhaf | Lee, Han Soo | Jeong, Jae-Soon | Cabrera, Jonathan SalarJournal of Marine Science and Engineering, Vol. 12 (2024), Iss. 1 P.177
https://doi.org/10.3390/jmse12010177 [Citations: 0] -
Low power computation of transoceanic wave propagation for tsunami hazard mitigation
Lavrentiev, Mikhail | Marchuk, Andrey | Oblaukhov, KonstantinOcean Modelling, Vol. 192 (2024), Iss. P.102459
https://doi.org/10.1016/j.ocemod.2024.102459 [Citations: 0] -
Numerical modeling of the long surface wave impact on a partially immersed structure in a coastal zone: Solitary waves over a flat slope
Gusev, O. I. | Khakimzyanov, G. S. | Skiba, V. S. | Chubarov, L. B.Physics of Fluids, Vol. 35 (2023), Iss. 8
https://doi.org/10.1063/5.0159984 [Citations: 2] -
Numerical model of the hydrowave laboratory for studying the interaction of sea waves with hydrotechnical structures
Нуднер, Игорь Сергеевич | Семенов, Константин Константинович | Лебедев, Владимир Валентинович | Хакимзянов, Гаяз Салимович | Захаров, Юрий НиколаевичВычислительные технологии, Vol. (2019), Iss. 1(24) P.86
https://doi.org/10.25743/ICT.2019.24.1.007 [Citations: 2] -
GROUP CLASSIFICATION OF THE TWO-DIMENSIONAL GREEN–NAGHDI EQUATIONS WITH A TIME-DEPENDENT BOTTOM TOPOGRAPHY
Meleshko, S. V. | Siriwat, P.Journal of Applied Mechanics and Technical Physics, Vol. 63 (2022), Iss. 6 P.972
https://doi.org/10.1134/S0021894422060086 [Citations: 1] -
Serre–Green–Naghdi Equations with Optimized Dispersion Properties Through a Modified Auxiliary Elliptic Equation
Cocquet, Pierre-Henri | Mihami, Fatima-Zahra | Moguen, Yann | Roeber, VolkerWater Waves, Vol. 6 (2024), Iss. 3 P.521
https://doi.org/10.1007/s42286-024-00100-7 [Citations: 0] -
Computational NAMI-DANCE complex in the problem of tsunami waves
Zaytsev, A.I. | Kurkin, A.A. | Pelinovsky, E.N. | Yalciner, A.Computational Continuum Mechanics, Vol. 12 (2019), Iss. 2 P.161
https://doi.org/10.7242/1999-6691/2019.12.2.14 [Citations: 0]