A Generalised Serre-Green-Naghdi equations for variable rectangular open channel hydraulics and its finite volume approximation
Preprint
Abstract
We present a non-linear dispersive shallow water model which enters in the framework of section-averaged models. These new equations are derived up to the second order of the shallow water approximation starting from the three-dimensional incompressible and irrotational Euler system. The derivation is carried out in the case of non uniform rectangular section and it generalises the well-known one-dimensional Serre-Green-Naghdi (SGN) equations on uneven bottom. The obtained model is fully consistent with the Euler system. We propose a well-balanced finite volume approximation and we present some numerical results to show the influence of the section variation.Keywords
All Related Versions
This publication has 16 references indexed in Scilit:
- A numerical scheme for an improved Green–Naghdi model in the Camassa–Holm regime for the propagation of internal wavesComputers & Fluids, 2017
- A new class of fully nonlinear and weakly dispersive Green–Naghdi models for efficient 2D simulationsJournal of Computational Physics, 2015
- A mathematical model for unsteady mixed flows in closed water pipesScience China Mathematics, 2012
- Numerical Simulation of Strongly Nonlinear and Dispersive Waves Using a Green–Naghdi ModelJournal of Scientific Computing, 2010
- Derivation of asymptotic two-dimensional time-dependent equations for surface water wave propagationPhysics of Fluids, 2009
- A fourth‐order compact finite volume scheme for fully nonlinear and weakly dispersive Boussinesq‐type equations. Part II: boundary conditions and validationInternational Journal for Numerical Methods in Fluids, 2006
- A finite volume solver for 1D shallow‐water equations applied to an actual riverInternational Journal for Numerical Methods in Fluids, 2001
- Numerical and experimental study of the transformation of a solitary wave over a shelf or isolated obstacleJournal of Fluid Mechanics, 1987
- A derivation of equations for wave propagation in water of variable depthJournal of Fluid Mechanics, 1976
- Calculations of the development of an undular boreJournal of Fluid Mechanics, 1966