A numerical scheme for an improved Green-Naghdi model in the Camassa-Holm regime for the propagation of internal waves

摘要

In this paper we introduce a new reformulation of the Green-Naghdi model in the Camassa-Holm regime for the propagation of internal waves over a flat topography derived by Duchene et al. [18]. These new Green-Naghdi systems are adapted to improve the frequency dispersion of the original model, they share the same order of precision as the standard one but have an appropriate structure which makes them much more suitable for the numerical resolution. We develop a second order splitting scheme where the hyperbolic part of the system is treated with a high-order finite volume scheme and the dispersive part is treated with a finite difference approach. Numerical simulations are then performed to validate the model and the numerical methods. (C) 2017 Elsevier Ltd. All rights reserved.