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Your search keyword '"Fully dispersive equations"' showing total 3 results
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3 results on '"Fully dispersive equations"'

1. The Whitham equation with surface tension.

Author

Dinvay, Evgueni, Moldabayev, Daulet, Dutykh, Denys, and Kalisch, Henrik

Abstract

The viability of the Whitham equation as a nonlocal model for capillary-gravity waves at the surface of an inviscid incompressible fluid is under study. A nonlocal Hamiltonian system of model equations is derived using the Hamiltonian structure of the free-surface water-wave problem and the Dirichlet-Neumann operator. The system features gravitational and capillary effects, and when restricted to one-way propagation, the system reduces to the capillary Whitham equation. It is shown numerically that in various scaling regimes the Whitham equation gives a more accurate approximation of the free-surface problem for the Euler system than other models like the KdV and Kawahara equation. In the case of relatively strong capillarity considered here, the KdV and Kawahara equations outperform the Whitham equation with surface tension only for very long waves with negative polarity. [ABSTRACT FROM AUTHOR]

Published
2017
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2. Numerical study of the Serre-Green-Naghdi equations and a fully dispersive counterpart

Author

Vincent Duchêne, Christian Klein, Institut de Recherche Mathématique de Rennes (IRMAR), AGROCAMPUS OUEST, Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Université de Rennes 1 (UR1), Université de Rennes (UNIV-RENNES)-Université de Rennes (UNIV-RENNES)-Université de Rennes 2 (UR2), Université de Rennes (UNIV-RENNES)-École normale supérieure - Rennes (ENS Rennes)-Centre National de la Recherche Scientifique (CNRS)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA), Centre National de la Recherche Scientifique (CNRS), Institut de Mathématiques de Bourgogne [Dijon] (IMB), Centre National de la Recherche Scientifique (CNRS)-Université de Franche-Comté (UFC), Université Bourgogne Franche-Comté [COMUE] (UBFC)-Université Bourgogne Franche-Comté [COMUE] (UBFC)-Université de Bourgogne (UB), Institut Universitaire de France (IUF), Ministère de l'Education nationale, de l’Enseignement supérieur et de la Recherche (M.E.N.E.S.R.), ANR-17-CE40-0035,ANuI,Approches analytiques, numériques et des systèmes intégrables pour les équations aux dérivées partielles dispersives nonlinéaires(2017), ANR-17-EURE-0002,EIPHI,Ingénierie et Innovation par les sciences physiques, les savoir-faire technologiques et l'interdisciplinarité(2017), European Project: 778010,IPaDEGAN, Université de Rennes (UR)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-École normale supérieure - Rennes (ENS Rennes)-Université de Rennes 2 (UR2)-Centre National de la Recherche Scientifique (CNRS)-INSTITUT AGRO Agrocampus Ouest, Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro), Université de Bourgogne (UB)-Université Bourgogne Franche-Comté [COMUE] (UBFC)-Centre National de la Recherche Scientifique (CNRS), French National Research Agency (ANR)ANuI -ANR-17-CE40-0035isite BFC project NAANoDEIPHI Graduate SchoolANR-17-EURE-0002European Commission778010, and ANR-11-LABX-0020,LEBESGUE,Centre de Mathématiques Henri Lebesgue : fondements, interactions, applications et Formation(2011)

Subjects
2020 MSC 65M70, 35Q35, 76B15, 35B35, Applied Mathematics, 010102 general mathematics, 65M70, 35Q35, 76B15, 35B35, 01 natural sciences, numerical investigation, 010305 fluids & plasmas, Mathematics - Analysis of PDEs, spectral methods, solitary waves, 0103 physical sciences, FOS: Mathematics, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], Discrete Mathematics and Combinatorics, Fully dispersive equations, 0101 mathematics, modulated oscillations, Green-Naghdi system, Analysis of PDEs (math.AP), Numerical experiments
Abstract

We perform numerical experiments on the Serre-Green-Naghdi (SGN) equations and a fully dispersive "Whitham-Green-Naghdi" (WGN) counterpart in dimension 1. In particular, solitary wave solutions of the WGN equations are constructed and their stability, along with the explicit ones of the SGN equations, is studied. Additionally, the emergence of modulated oscillations and the possibility of a blow-up of solutions in various situations is investigated. We argue that a simple numerical scheme based on a Fourier spectral method combined with the Krylov subspace iterative technique GMRES to address the elliptic problem and a fourth order explicit Runge-Kutta scheme in time allows to address efficiently even computationally challenging problems., To appear in DCDS-B. Figures are reproducible using the Julia package WaterWaves1D at https://github.com/WaterWavesModels/

Published
2022
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3. The Whitham Equation with Surface Tension

Author

Henrik Kalisch, Denys Dutykh, Evgueni Dinvay, Daulet Moldabayev, Department of Mathematics, University of Bergen (UiB), Laboratoire de Mathématiques (LAMA), Centre National de la Recherche Scientifique (CNRS)-Université Savoie Mont Blanc (USMB [Université de Savoie] [Université de Chambéry]), Institut National des Sciences Mathématiques et de leurs Interactions (INSMI), and Université Savoie Mont Blanc (USMB [Université de Savoie] [Université de Chambéry])

Subjects
[PHYS.PHYS.PHYS-FLU-DYN]Physics [physics]/Physics [physics]/Fluid Dynamics [physics.flu-dyn], Mathematics::Analysis of PDEs, Aerospace Engineering, FOS: Physical sciences, Ocean Engineering, 01 natural sciences, 010305 fluids & plasmas, Hamiltonian system, Surface tension, [PHYS.PHYS.PHYS-COMP-PH]Physics [physics]/Physics [physics]/Computational Physics [physics.comp-ph], Physics::Fluid Dynamics, Mathematics - Analysis of PDEs, [NLIN.NLIN-PS]Nonlinear Sciences [physics]/Pattern Formation and Solitons [nlin.PS], Inviscid flow, 0103 physical sciences, FOS: Mathematics, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], Fully dispersive equations, [PHYS.MECA.MEFL]Physics [physics]/Mechanics [physics]/Fluid mechanics [physics.class-ph], Mathematics - Numerical Analysis, 0101 mathematics, Electrical and Electronic Engineering, Hamiltonian systems, Korteweg–de Vries equation, Nonlinear Sciences::Pattern Formation and Solitons, Physics, [PHYS.PHYS.PHYS-AO-PH]Physics [physics]/Physics [physics]/Atmospheric and Oceanic Physics [physics.ao-ph], Whitham equation, Applied Mathematics, Mechanical Engineering, 010102 general mathematics, Mathematical analysis, Fluid Dynamics (physics.flu-dyn), Numerical Analysis (math.NA), Physics - Fluid Dynamics, Euler system, Computational Physics (physics.comp-ph), Surface waves, 3. Good health, Physics - Atmospheric and Oceanic Physics, Nonlinear Sciences::Exactly Solvable and Integrable Systems, Control and Systems Engineering, Capillarity, Free surface, Atmospheric and Oceanic Physics (physics.ao-ph), Compressibility, Physics - Computational Physics, Analysis of PDEs (math.AP)
Abstract

The viability of the Whitham equation as a nonlocal model for capillary-gravity waves at the surface of an inviscid incompressible fluid is under study. A nonlocal Hamiltonian system of model equations is derived using the Hamiltonian structure of the free surface water wave problem and the Dirichlet-Neumann operator. The system features gravitational and capillary effects, and when restricted to one-way propagation, the system reduces to the capillary Whitham equation. It is shown numerically that in various scaling regimes the Whitham equation gives a more accurate approximation of the free-surface problem for the Euler system than other models like the KdV, and Kawahara equation. In the case of relatively strong capillarity considered here, the KdV and Kawahara equations outperform the Whitham equation with surface tension only for very long waves with negative polarity., 19 pages, 5 figures, 1 table, 36 references. Other author's papers can be downloaded at http://www.denys-dutykh.com/. arXiv admin note: text overlap with arXiv:1410.8299

Published
2020
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