A numerical scheme for an improved Green–Naghdi model in the Camassa–Holm regime for the propagation of internal waves. (12th October 2017)

• Record Type: Journal Article
• Authors: Bourdarias, Christian; Gerbi, Stéphane; Lteif, Ralph
• Is Part Of: Computers & fluids. Volume 156(2017)
• Page Start: 283
• Page End: 304
• Publication Date: 2017-10-12
• Subjects: Green–Naghdi model -- Nonlinear shallow water -- Dispersive waves -- Nonlinear interactions -- Improved dispersion -- Splitting method -- Hybrid method -- Finite volume -- Finite difference -- High order scheme -- WENO Reconstruction; Fluid dynamics -- Data processing -- Periodicals; 532.050285
• DOI: 10.1016/j.compfluid.2017.07.012
• Languages: English
• ISSNs: 0045-7930

Abstract

Highlights: Derivation of Green–Naghdi model with improved frequency dispersion. Implementation of a second order splitting method: the conservative part and the dispersive part. Hybrid method of discretization: Finite volume and finite difference. High order schemes using WENO reconstruction. Numerical tests cases validate the model and the numerical methods. Abstract: 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 Duchêne 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.