Long-time effects of bottom topography in shallow water
Physica D - Special issue on nonlinear phenomena in ocean dynamics
The Runge-Kutta discontinuous Galerkin method for conservation laws V multidimensional systems
Journal of Computational Physics
Journal of Computational Physics
WENO schemes for balance laws with spatially varying flux
Journal of Computational Physics
Journal of Computational Physics
Journal of Scientific Computing
SIAM Journal on Numerical Analysis
A High-Order Spectral Method for Nonlinear Water Waves over Moving Bottom Topography
SIAM Journal on Scientific Computing
Numerical simulation of three-dimensional nonlinear water waves
Journal of Computational Physics
A Central Discontinuous Galerkin Method for Hamilton-Jacobi Equations
Journal of Scientific Computing
A splitting approach for the fully nonlinear and weakly dispersive Green-Naghdi model
Journal of Computational Physics
Finite volume schemes for dispersive wave propagation and runup
Journal of Computational Physics
Journal of Computational Physics
Numerical Simulation of Strongly Nonlinear and Dispersive Waves Using a Green---Naghdi Model
Journal of Scientific Computing
Journal of Computational Physics
Hi-index | 31.45 |
In this paper, we consider a one-dimensional fully nonlinear weakly dispersive Green-Naghdi model for shallow water waves over variable bottom topographies. Such model describes a large spectrum of shallow water waves, and it is thus of great importance to design accurate and robust numerical methods for solving it. The governing equations contain mixed spatial and temporal derivatives of the unknowns. They also have still-water stationary solutions which should be preserved in stable numerical simulations. In our numerical approach, we first reformulate the Green-Naghdi equations into balance laws coupled with an elliptic equation. We then propose a family of high order numerical methods which discretize the balance laws with well-balanced central discontinuous Galerkin methods and the elliptic part with continuous finite element methods. Linear dispersion analysis for both the (reformulated) Green-Naghdi system and versions of the proposed numerical scheme is performed when the bottom topography is flat. Numerical tests are presented to illustrate the accuracy and stability of the proposed schemes as well as the capability of the Green-Naghdi model to describe a wide range of shallow water wave phenomena.