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Bonneton, P., Barthelemy, E., Chazel, F., Cienfuegos, R., Lannes, D., Marche, F. and Tissier, M. (2011) Recent Advances in Serre-Green Naghdi Modelling for Wave Transformation, Breaking and Runup Processes. Journal of Computational Physics, 30, 589-597.

has been cited by the following article:

• TITLE: A Central Numerical Scheme to 1D Green-Naghdi Wave Equations

  AUTHORS: Kezhao Fang, Zifeng Jiao, Jing Yin, Jiawen Sun

  KEYWORDS: Green-Naghdi Equations, Finite-Volume Method, Solitary Wave

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.3 No.8, August 26, 2015

  ABSTRACT: A numerical scheme based on hybrid central finite-volume and finite-difference method is presented to model Green-Naghdi water wave equations. The governing equations are reformulated into the conservative form, and the convective flux is estimated using a Godunov-type finite volume method while the remaining terms are discretized using finite difference method. To enhance the robustness of the model, a central-upwind flux evaluation and a well-balanced non- negative water depth construction are incorporated. Numerical tests demonstrate that present model has the advantages of stability preserving and numerical efficiency.