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

作者：Bourdarias Christian; Gerbi Stephane^*; Lteif Ralph

来源：Computers & Fluids, 2017, 156: 283-304.

DOI：10.1016/j.compfluid.2017.07.012

• 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

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.

• 出版日期2017-10-12