B. Alvarez-samaniego and D. Lannes, A Nash-Moser theorem for singular evolution equations. Application to the Serre and Green-Naghdi equations, ndiana University Mathematics Journal, issue.57, pp.97-131, 2011.
URL : https://hal.archives-ouvertes.fr/hal-00281508

P. Bonneton, E. Barthelemy, F. Chazel, R. Cienfuegos, D. Lannes et al., Recent advances in Serre???Green Naghdi modelling for wave transformation, breaking and runup processes, European Journal of Mechanics - B/Fluids, vol.30, issue.6, pp.589-597, 2011.
DOI : 10.1016/j.euromechflu.2011.02.005
URL : https://hal.archives-ouvertes.fr/hal-00606543

A. Chertok, S. Cui, A. Kurganov, and T. Wu, Steady state and sign preserving semiimplicit Runge-Kutta methods for ODEs with stiff damping term, Siam Journal of Numerical Analysis, issue.53, pp.2008-2029, 2015.

A. Filippini, Free surface flow simulation in estuarine and coastal environments: numerical development and application on unstructured mehes, 2016.

A. G. Filippini, M. Kazolea, and M. Ricchiuto, A flexible genuinely nonlinear approach for nonlinear wave propagation, breaking and run-up, Journal of Computational Physics, vol.310, issue.310, pp.381-417, 2016.
DOI : 10.1016/j.jcp.2016.01.027

A. E. Green and A. Naghdi, A derivation of equations for wave propagation in water of variable depth, Journal of Fluid Mechanics, vol.338, issue.02, pp.237-246, 1976.
DOI : 10.1017/S0022112076002425

M. A. Walkley and M. Berzins, A finite element method for the two-dimensional extended Boussinesq equations, International Journal for Numerical Methods in Fluids, vol.7, issue.10, pp.865-886, 2002.
DOI : 10.1002/fld.349

M. Kazolea, A. I. Delis, I. Nikolos, and S. C. , An unstructured finite volume numerical scheme for extended 2D Boussinesq-type equations, Coastal Engineering, vol.69, issue.69, pp.42-66, 2012.
DOI : 10.1016/j.coastaleng.2012.05.008

M. Kazolea, A. I. Delis, and S. C. , Numerical treatment of wave breaking on unstructured finite volume approximations for extended Boussinesq-type equations, Journal of Computational Physics, vol.271, issue.271, pp.281-305, 2014.
DOI : 10.1016/j.jcp.2014.01.030

D. Lannes and F. Marche, A new class of fully nonlinear and weakly dispersive Green???Naghdi models for efficient 2D simulations, Journal of Computational Physics, vol.282, issue.282, pp.238-268, 2015.
DOI : 10.1016/j.jcp.2014.11.016
URL : https://hal.archives-ouvertes.fr/hal-00932858

M. Ricchiuto and A. Filippini, Upwind residual discretization of enhanced Boussinesq equations for wave propagation over complex bathymetries, Journal of Computational Physics, vol.271, issue.271, pp.306-341, 2014.
DOI : 10.1016/j.jcp.2013.12.048
URL : https://hal.archives-ouvertes.fr/hal-00826912

C. E. Synolakis, The run-up of solitary waves, J. Fluid Mech, issue.185, pp.532-545, 1987.

M. Tonelli and M. Petti, Hybrid finite volume ??? finite difference scheme for 2DH improved Boussinesq equations, Coastal Engineering, vol.56, issue.5-6, 2009.
DOI : 10.1016/j.coastaleng.2009.01.001

P. Roe, Approximate Riemann solvers, parameter vectors, and difference schemes, J.Comput.Phys, issue.43, pp.357-372, 1982.
DOI : 10.1016/0021-9991(81)90128-5
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.457.5978

. Van-leer, Towards the ultimate conservative difference scheme III. Upstream-centered finite-difference schemes for ideal compressible flow, Journal of Computational Physics, vol.23, issue.3, pp.263-275, 1977.
DOI : 10.1016/0021-9991(77)90094-8

G. Wei and J. T. Kirby, Time-Dependent Numerical Code for Extended Boussinesq Equations, Journal of Waterway, Port, Coastal, and Ocean Engineering, vol.121, issue.5, pp.251-261, 1995.
DOI : 10.1061/(ASCE)0733-950X(1995)121:5(251)

G. Wei, J. T. Kirby, S. Grilli, and R. Subramanya, A fully nonlinear Boussinesq model for surface waves. Part 1. Highly nonlinear unsteady waves, Journal of Fluid Mechanics, vol.107, issue.-1, pp.71-92, 1995.
DOI : 10.1063/1.865459

G. Wei, J. T. Kirby, and A. Sinha, Generation of waves in Boussinesq models using a source function method, Coastal Engineering, vol.36, issue.4, pp.271-299, 1999.
DOI : 10.1016/S0378-3839(99)00009-5

R. W. Whalin, The limit of applicability of linear wave refraction theory in a convergence zone, 1971.