Dispersive nonlinear shallow-water equations: some preliminary numerical results

DOI10.1007/s10665-009-9328-5zbMath1333.76052OpenAlexW2071463454MaRDI QIDQ980714

Giovanna Grosso, Matteo Antuono, Maurizio Brocchini

Publication date: 29 June 2010

Published in: Journal of Engineering Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10665-009-9328-5

zbMATH Keywords

wavesBoussinesq equationsnonlinear shallow-water equationsdispersive nonlinear shallow-water equationsfinite-volume solversnearshore

Mathematics Subject Classification ID

Water waves, gravity waves; dispersion and scattering, nonlinear interaction (76B15) Finite volume methods applied to problems in fluid mechanics (76M12) Finite volume methods for initial value and initial-boundary value problems involving PDEs (65M08)

Related Items

A hyperbolic reformulation of the Serre-Green-Naghdi model for general bottom topographies ⋮ Numerical simulations of a dispersive model approximating free-surface Euler equations ⋮ Multilayer shallow model for dry granular flows with a weakly non-hydrostatic pressure ⋮ Alternative forms of enhanced Boussinesq equations with improved nonlinearity ⋮ An efficient hyperbolic relaxation system for dispersive non-hydrostatic water waves and its solution with high order discontinuous Galerkin schemes ⋮ Hyperbolic model for free surface shallow water flows with effects of dispersion, vorticity and topography ⋮ On high order ADER discontinuous Galerkin schemes for first order hyperbolic reformulations of nonlinear dispersive systems

Cites Work

• Unnamed Item
• Unnamed Item
• Arbitrary high order non-oscillatory finite volume schemes on unstructured meshes for linear hyperbolic systems
• Uniformly high order accurate essentially non-oscillatory schemes. III
• Upwind methods for hyperbolic conservation laws with source terms
• Finite volume schemes of very high order of accuracy for stiff hyperbolic balance laws
• Surf and run-up on a beach: a uniform bore
• Dispersive Nonlinear Shallow-Water Equations
• A fully nonlinear Boussinesq model for surface waves. Part 1. Highly nonlinear unsteady waves
• On the well-balance property of Roe's method for nonconservative hyperbolic systems. applications to shallow-water systems
• High order finite volume schemes based on reconstruction of states for solving hyperbolic systems with nonconservative products. Applications to shallow-water systems
• A fourth-order compact finite volume scheme for fully nonlinear and weakly dispersive Boussinesq-type equations. Part I: model development and analysis
• Long waves in a uniform channel of arbitrary cross-section
• Hybrid finite-volume finite-difference scheme for the solution of Boussinesq equations

This page was built for publication: Dispersive nonlinear shallow-water equations: some preliminary numerical results