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

## TL;DR

This paper introduces a reformulated Green-Naghdi model tailored for internal wave propagation in the Camassa-Holm regime, enhancing numerical resolution and dispersion properties, validated through a second order splitting scheme and simulations.

## Contribution

The paper presents a new reformulation of the Green-Naghdi model that improves numerical stability and dispersion characteristics for internal wave simulations.

## Key findings

- Enhanced frequency dispersion in the new model
- Second order splitting scheme effectively solves the system
- Numerical simulations validate the improved model and method

## 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 Duch\^ene, Israwi and Talhouk. 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.