A combined finite volume -finite element scheme for a dispersive shallow water system, Networks and Heterogeneous Media (NHM), 2016. ,
URL : https://hal.archives-ouvertes.fr/hal-01160718
A fast and stable well-balanced scheme with hydrostatic reconstruction for shallow water flows, SIAM J. Sci. Comput, vol.25, pp.2050-2065, 2004. ,
A well-balanced positivity preserving "second-order" scheme for shallow water flows on unstructured meshes, Journal of Computational Physics, vol.206, pp.311-333, 2005. ,
URL : https://hal.archives-ouvertes.fr/inria-00070738
A splitting approach for the fully nonlinear and weakly dispersive Green-Naghdi model, Journal of Computational Physics, vol.230, pp.1479-1498, 2011. ,
URL : https://hal.archives-ouvertes.fr/hal-00482564
Nonlinear stability of finite volume methods for hyperbolic conservation laws, and well-balanced schemes for sources, 2004. ,
An energyconsistent depth-averaged Euler system: Derivation and properties, Discrete and Continuous Dynamical Systems -Series B, vol.20, pp.961-988, 2015. ,
URL : https://hal.archives-ouvertes.fr/hal-01011691
Error estimate for time-explicit finite volume approximation of strong solutions to systems of conservation laws, SIAM Journal on Numerical Analysis, vol.54, pp.1263-1287, 2016. ,
, Open-channel hydraulics, 1959.
Numerical Simulation of Strongly Nonlinear and Dispersive Waves Using a Green-Naghdi Model, Journal of Scientific Computing, vol.48, pp.105-116, 2010. ,
URL : https://hal.archives-ouvertes.fr/hal-00482561
A fourth-order compact finite volume scheme for fully nonlinear and weakly dispersive Boussinesq-type equations. Part I: model development and analysis, International Journal for Numerical Methods in Fluids, vol.51, pp.1217-1253, 2006. ,
URL : https://hal.archives-ouvertes.fr/hal-00182841
A robust entropysatisfying finite volume scheme for the isentropic Baer-Nunziato model, ESAIM: Mathematical Modelling and Numerical Analysis, vol.48, pp.165-206, 2013. ,
URL : https://hal.archives-ouvertes.fr/hal-00795568
Error estimates of finite difference schemes for the Korteweg-de Vries equation, 2018. ,
Théorie du mouvement non permanent des eaux, avec application aux crues des rivières et à l'introduction des marées dans leurs lits, C.R. Acad. Sci, vol.73, pp.147-154, 1871. ,
Discontinuous-galerkin discretization of a new class of green-naghdi equations, Communications in Computational Physics, vol.17, pp.721-760, 2015. ,
Convergence of a higher order scheme for the korteweg-de vries equation, SIAM Journal on Numerical Analysis, vol.53, pp.1963-1983, 2015. ,
A rapid numerical method for solving serregreen-naghdi equations describing long free surface gravity waves, Nonlinearity, p.2718, 2017. ,
A hierarchy of dispersive layer-averaged approximations of Euler equations for free surface flows, Communications in Mathematical Sciences, vol.16, pp.1169-1202, 2018. ,
Numerical modeling of twophase flows using the two-fluid two-pressure approach, Mathematical Models and Methods in Applied Sciences, vol.14, pp.663-700, 2004. ,
Derivation of viscous saint-venant system for laminar shallow water; numerical validation, Discrete and Continuous Dynamical Systems -Series B, vol.1, pp.89-102, 2001. ,
Numerical approximation of hyperbolic systems of conservation laws, Applied Mathematical Sciences, vol.118, 1996. ,
A difference method for numerical calculation of discontinuous solutions of the equations of hydrodynamics, Mat. Sb, pp.271-306, 1959. ,
A derivation of equations for wave propagation in water of variable depth, Journal of Fluid Mechanics, vol.78, pp.237-246, 1976. ,
An overview of projection methods for incompressible flows, Computer Methods in Applied Mechanics and Engineering, vol.195, pp.6011-6045, 2006. ,
, Operator splitting for partial differential equations with burgers nonlinearity, Mathematics of Computation, vol.82, pp.173-185, 2012.
Derivation of asymptotic two-dimensional timedependent equations for surface water wave propagation, Physics of Fluids, p.21, 2009. ,
A new class of fully nonlinear and weakly dispersive Green-Naghdi models for efficient 2D simulations, Journal of Computational Physics, vol.282, pp.238-268, 2015. ,
A numerical scheme for the Green-Naghdi model, Journal of Computational Physics, vol.229, pp.2034-2045, 2010. ,
Finite volume methods for hyperbolic problems, vol.31, 2002. ,
High order well-balanced cdg-fe methods for shallow water waves by a green-naghdi model, Journal of Computational Physics, vol.257, pp.169-192, 2014. ,
On the galerkin/finite-element method for the serre equations, Journal of Scientific Computing, pp.166-195, 2014. ,
URL : https://hal.archives-ouvertes.fr/hal-00834064
Centered-potential regularization for the advection upstream splitting method, SIAM Journal on Numerical Analysis, vol.54, pp.3083-3104, 2016. ,
URL : https://hal.archives-ouvertes.fr/hal-01152395
Long waves on a beach, Journal of Fluid Mechanics, vol.27, pp.815-827, 1967. ,
A kinetic scheme for the saint-venant system with a source term, Calcolo, vol.38, pp.201-231, 2001. ,
Upwind residual discretization of enhanced boussinesq equations for wave propagation over complex bathymetries, Frontiers in Computational Physics, vol.271, pp.306-341, 2014. ,
, Contribution à l'étude des écoulements permanents et variables dans les canaux, pp.830-872, 1953.
Level set methods for fluid interfaces, Annual Review of Fluid Mechanics, vol.35, pp.341-372, 2003. ,
On modelling phase transitions by means of rate-type constitutive equations. shock wave structure, International Journal of Engineering Science, vol.28, pp.829-841, 1990. ,
Riemann solvers and numerical methods for fluid dynamics: a practical introduction, 2013. ,
A second-order accurate pressure-correction scheme for viscous incompressible flow, SIAM Journal on Scientific and Statistical Computing, vol.7, pp.870-891, 1986. ,
Towards the ultimate conservative difference scheme. v. a secondorder sequel to godunov's method, Journal of Computational Physics, vol.32, pp.101-136, 1979. ,
Depth-integrated, nonhydrostatic model for wave breaking and run-up, International Journal for Numerical Methods in Fluids, pp.473-497, 2009. ,