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Le Metayer, O., Gavrilyuk, S. and Hank, S. (2010) A numerical scheme for the Green-Naghdi model. Journal of Computational Physics, 229, 2034-2045. Bonneton, P., Barthelemy, E., Chazel, F., Cienfuegos, R., Lannes, D., Marche, F., and Tissier, M. (2011) Recent in Serre-Green Naghdi modelling for wave transformation, breaking and runup processes. Journal of Physics, 30, 589-597. Li, M., Guyenne, P., Li, F. and Xu, L. (2014) High Order Well-Balanced CDG–FE Methods for Shallow Water Waves by A Green–Naghdi Model. J. of Computational Physics, 257, 169-192. Fang, K., Liu, Z., and Zou, Z. (2015) Fully Nonlinear Modeling Wave Transformation over Fringing Reefs Using Shock-Capturing Boussinesq Model. Journal of Coastal Research, in press. Wang, Y., Liang, Q., Kesserwani, G. and Hall, J. W. (2011) A 2D Shallow Flow Model for Practical Dam-Break Journal of Hydraulic Research, 49, 307-316. Kurganov, A. and Petrova, G. (2007) A Second-order Well-balanced Positivity Preserving Central Upwind Scheme for the Saint-Vinant System. Commun. Math. Sci. 5, 133–160. Lannes, D. and Marche, F. (2015) A New Class of Fully Nonlinear and Weakly Dispersive Green–Naghdi Models for Efficient 2D Simulations. Journal of Computational Physics, 282, 238-268. Craig, W., Guyenne, P., Hammack, J., Henderson, D. and Sulem, C. (2006) Solitary Water Wave Interactions. Physics of Fluids (1994-present), 18, 057106. Synolakis, C. E. (1986) The runup of long waves (Doctoral dissertation, California Institute of Technology).