Numerical simulation of strongly nonlinear and dispersive waves using a Green-Naghdi model

DOI10.1007/s10915-010-9395-9zbMath1419.76454OpenAlexW2137588198MaRDI QIDQ554663

Fabien Marche, David Lannes, Florent Chazel

Publication date: 4 August 2011

Published in: Journal of Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10915-010-9395-9

zbMATH Keywords

hyperbolic systemsdispersive wavessplitting techniquenonlinear interactionshybrid methodGreen-Naghdi equationsWENO reconstructionhighorder well-balanced schemesubmerged bar

Mathematics Subject Classification ID

Water waves, gravity waves; dispersion and scattering, nonlinear interaction (76B15) Finite difference methods applied to problems in fluid mechanics (76M20) Finite volume methods applied to problems in fluid mechanics (76M12)

Related Items

Combined hybridizable discontinuous Galerkin (HDG) and Runge-Kutta discontinuous Galerkin (RK-DG) formulations for Green-Naghdi equations on unstructured meshes, A Class of Boundary Conditions for Time-Discrete Green--Naghdi Equations with Bathymetry, A flexible genuinely nonlinear approach for nonlinear wave propagation, breaking and run-up, A reconstructed central discontinuous Galerkin-finite element method for the fully nonlinear weakly dispersive Green-Naghdi model, A combined finite volume -- finite element scheme for a dispersive shallow water system, An ADER-type scheme for a class of equations arising from the water-wave theory, A numerical scheme for an improved Green-Naghdi model in the Camassa-Holm regime for the propagation of internal waves, High order well-balanced CDG-FE methods for shallow water waves by a Green-Naghdi model, A new class of higher-ordered/extended Boussinesq system for efficient numerical simulations by splitting operators, Numerical simulations of a non-hydrostatic shallow water model, Numerical simulations of a dispersive model approximating free-surface Euler equations, A new symmetric interior penalty discontinuous Galerkin formulation for the <scp>Serre–Green–Naghdi</scp> equations, A Review of Nonlinear Boussinesq-Type Models for Coastal Ocean Modeling, Extended Lagrangian approach for the numerical study of multidimensional dispersive waves: applications to the Serre-Green-Naghdi equations, On the accurate simulation of nearshore and dam break problems involving dispersive breaking waves, Recent advances in Serre-Green-Naghdi modelling for wave transformation, breaking and runup processes, The VOLNA code for the numerical modeling of tsunami waves: generation, propagation and inundation, Modeling shallow water waves, A splitting approach for the fully nonlinear and weakly dispersive Green-Naghdi model, Weighted interior penalty discretization of fully nonlinear and weakly dispersive free surface shallow water flows, Wave breaking in Boussinesq models for undular bores, The solution of nonlinear Green-Naghdi equation arising in water sciences via a meshless method which combines moving Kriging interpolation shape functions with the weighted essentially non-oscillatory method, A SOLUTION OF THE CONSERVATION LAW FORM OF THE SERRE EQUATIONS, A new model of shoaling and breaking waves: one-dimensional solitary wave on a mild sloping beach, A two-dimensional method for a family of dispersive shallow water models, Dispersive and dispersive-like bores in channels with sloping banks, A CDG-FE method for the two-dimensional Green-Naghdi model with the enhanced dispersive property, On the Galerkin/finite-element method for the Serre equations, High order well-balanced central local discontinuous Galerkin-finite element methods for solving the Green-Naghdi model, Dispersive Shallow Water Wave Modelling. Part II: Numerical Simulation on a Globally Flat Space, An efficient two-layer non-hydrostatic approach for dispersive water waves, Nonlinear Wave–Current Interactions in Shallow Water, An energy-consistent depth-averaged Euler system: derivation, A new model of shoaling and breaking waves. Part 2. Run-up and two-dimensional waves, Discontinuous Galerkin methods for a dispersive wave hydro-sediment-morphodynamic model, A new class of fully nonlinear and weakly dispersive Green-Naghdi models for efficient 2D simulations, A comparative study of diffraction of shallow-water waves by high-level IGN and GN equations, A discontinuous Galerkin method for a new class of Green-Naghdi equations on simplicial unstructured meshes, Numerical solution of the fully non-linear weakly dispersive Serre equations for steep gradient flows, An improved Serre model: efficient simulation and comparative evaluation, An extension of the Boussinesq-type models to weakly compressible flows, Fully dispersive Boussinesq models with uneven bathymetry, An explicit hybridized discontinuous Galerkin method for Serre-Green-Naghdi wave model, Finite volume and pseudo-spectral schemes for the fully nonlinear 1D Serre equations, A Generalised Serre-Green-Naghdi Equations for Variable Rectangular Open Channel Hydraulics and Its Finite Volume Approximation, Application of a Combined Finite Element—Finite Volume Method to a 2D Non-hydrostatic Shallow Water Problem, Asymptotic shallow water models with non smooth topographies

Cites Work

• A splitting approach for the fully nonlinear and weakly dispersive Green-Naghdi model
• Large deformation of liquid capsules enclosed by thin shells immersed in the fluid
• Numerical approximation of hyperbolic systems of conservation laws
• Efficient implementation of weighted ENO schemes
• The kinematics and stability of solitary and cnoidal wave solutions of the Serre equations
• Large time existence for 3D water waves and asymptotics
• Well-balanced finite volume schemes of arbitrary order of accuracy for shallow water flows
• A Petrov-Galerkin finite element model for one-dimensional fully non-linear and weakly dispersive wave propagation
• A Positive Preserving High Order VFRoe Scheme for Shallow Water Equations: A Class of Relaxation Schemes
• A fourth-order compact finite volume scheme for fully nonlinear and weakly dispersive Boussinesq-type equations. Part II: boundary conditions and validation
• A double-layer Boussinesq-type model for highly nonlinear and dispersive waves
• A derivation of equations for wave propagation in water of variable depth
• A Fast and Stable Well-Balanced Scheme with Hydrostatic Reconstruction for Shallow Water Flows
• Korteweg-de Vries Equation and Generalizations. III. Derivation of the Korteweg-de Vries Equation and Burgers Equation
• A fully nonlinear Boussinesq model for surface waves. Part 1. Highly nonlinear unsteady waves
• Derivation of asymptotic two-dimensional time-dependent equations for surface water wave propagation
• A fourth-order compact finite volume scheme for fully nonlinear and weakly dispersive Boussinesq-type equations. Part I: model development and analysis
• A technique of treating negative weights in WENO schemes