Journal ArticleDOI
A new approach to handle wave breaking in fully non-linear Boussinesq models
TLDR
In this article, a new method to handle wave breaking in fully non-linear Boussinesq-type models is presented, based on a reformulation of the set of governing equations (namely Serre Green-Naghdi equations) that allows us to split them into a hyperbolic part in the conservative form and a dispersive part.About:
This article is published in Coastal Engineering.The article was published on 2012-09-01. It has received 140 citations till now. The article focuses on the topics: Breaking wave & Shallow water equations.read more
Citations
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Journal ArticleDOI
A quadtree-adaptive multigrid solver for the Serre-Green-Naghdi equations
TL;DR: A novel combination of methods for the numerical approximation of solutions to the Serre-Green-Naghdi equations preserves the robustness of the original finite-volume Saint-Venant solver, in particular for the treatment of wetting/drying and equilibrium states.
Journal ArticleDOI
Depth-induced wave breaking in a non-hydrostatic, near-shore wave model
TL;DR: In this article, the authors assume a hydrostatic pressure distribution at the front of a breaking wave, which ensures that the wave front develops a vertical face and conserves mass and momentum.
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A modeling-based analysis of the flooding associated with Xynthia, central Bay of Biscay
TL;DR: In this article, a 2DH fully coupled modeling system is applied to the North-East Atlantic Ocean, with a resolution locally reaching a few meters along the coastline of the study area.
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Boussinesq Models and Their Application to Coastal Processes across a Wide Range of Scales
TL;DR: In this paper, the development of a class of depth-integrated, phase-resolving models for surface wave propagation, known as Boussinesq-type models (BTMs), is reviewed.
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A new class of fully nonlinear and weakly dispersive Green-Naghdi models for efficient 2D simulations
David Lannes,Fabien Marche +1 more
TL;DR: A new class of two-dimensional fully nonlinear and weakly dispersive Green-Naghdi equations over varying topography that have a mathematical structure which makes them much more suitable for the numerical resolution, in particular in the demanding case of two dimensional surfaces.
References
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Journal ArticleDOI
Modelling storm impacts on beaches, dunes and barrier islands
Dano Roelvink,Dano Roelvink,Ad Reniers,Ad Reniers,Ap van Dongeren,Jaap van Thiel de Vries,Robert McCall,Jamie Lescinski +7 more
TL;DR: In this paper, a nearshore numerical model approach to assess the natural coastal response during time-varying storm and hurricane conditions, including dune erosion, overwash and breaching, is validated with a series of analytical, laboratory and field test cases.
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Alternative form of Boussinesq equations for nearshore wave propagation
TL;DR: In this paper, a new form of the Boussinesq equations is derived using the velocity at an arbitrary distance from the still water level as the velocity variable instead of the commonly used depth-averaged velocity.
Book
Water Waves: The Mathematical Theory with Applications
TL;DR: In this article, two-dimensional waves on a running stream in water of uniform depth were modeled as a moving pressure point, and the theory of the wave pattern created by a moving ship was proposed.
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A Fast and Stable Well-Balanced Scheme with Hydrostatic Reconstruction for Shallow Water Flows
TL;DR: A general strategy is described, based on a local hydrostatic reconstruction, that allows a well-balanced scheme to derive from any given numerical flux for the homogeneous problem, whenever the initial solver satisfies some classical stability properties.
Journal ArticleDOI
A fully nonlinear Boussinesq model for surface waves. Part 1. Highly nonlinear unsteady waves
TL;DR: In this paper, a high-order numerical model based on the Boussinesq model was developed and applied to the study of two canonical problems: solitary wave shoaling on slopes and undular bore propagation over a horizontal bed.