,
Hybrid numerical methods to solve shallow water equations for hurricane induced storm surge modeling, Environmental Modelling & Software, vol.46, pp.118-128, 2013. ,
An L2 stable approximation of the Navier Stokes convection operator for low order non conforming finite elements, International Journal for Numerical Methods in Fluids, vol.66, issue.5, pp.555-580, 2011. ,
A fast and stable well-balanced scheme with hydrostatic reconstruction for shallow water flows, SIAM J. Sci. Comput, vol.25, pp.2050-2065, 2004. ,
Analysis of modified Godunov type schemes for the twodimensional linear wave equation with Coriolis source term on cartesian meshes, Journal of Computational Physics, vol.373, pp.91-129, 2018. ,
URL : https://hal.archives-ouvertes.fr/hal-01618753
Upwind methods for hyperbolic conservation laws with source terms, Comput. & Fluids, vol.23, pp.1049-1071, 1994. ,
Efficient well balanced hydrostatic upwind schemes for shallow water equations, J. Comput. Phys, vol.231, pp.4993-5015, 2012. ,
An oceanic general circulation model framed in hybrid isopycnic-cartesian coordinates, Ocean Model, vol.4, pp.55-88, 2002. ,
Finite volume evolution Galerkin methods for the shallow water equations with dry beds, Commun. Comput. Phys, vol.10, issue.2, pp.371-404, 2011. ,
Unstructured finite volume discretization of bed friction and convective flux in solute transport models linked to the shallow water equations, Journal of Computational Physics, vol.231, pp.3317-3339, 2012. ,
An explicit asymptotic preserving low froude scheme for the multilayer shallow water model with density stratification, Journal of Computational Physics, vol.343, pp.235-270, 2017. ,
URL : https://hal.archives-ouvertes.fr/hal-01340629
Numerical treatment of wet/dry fronts in shallow flows with a modified Roe scheme, Mathematical Models and Methods in Applied Sciences, vol.16, issue.6, pp.897-931, 2006. ,
High order exactly well-balanced numerical methods for shallow water systems, Journal of Computational Physics, vol.246, pp.242-264, 2013. ,
Well-balanced numerical schemes based on a generalized hydrostatic reconstruction technique, Mathematical Models and Methods in Applied Sciences, vol.17, pp.2055-2113, 2007. ,
A staggered semi-implicit spectral discontinuous Galerkin scheme for the shallow water equations, Applied Mathematics and Computation, vol.219, issue.15, pp.8057-8077, 2013. ,
Recent advances on the discontinuous Galerkin method for shallow water equations with topography source terms, Computers & Fluids, pp.88-104, 2013. ,
URL : https://hal.archives-ouvertes.fr/hal-00998024
Semi-implicit staggered mesh scheme for the multi-layer shallow water system, C. R. Acad. Sci. Paris, vol.355, pp.1298-1306, 2017. ,
URL : https://hal.archives-ouvertes.fr/hal-02081576
A well-balanced Runge-Kutta discontinuous Galerkin method for the shallow-water equations with flooding and drying, Int. J. Numer. Meth. Fluids, vol.58, pp.1-25, 2008. ,
URL : https://hal.archives-ouvertes.fr/hal-00153788
On the staggered scheme for shallow water model down an inclined channel, AIP Conference Proceedings, pp.1867-020002, 2017. ,
Well-balanced and energy stable schemes for the shallow water equations with discontinuous topography, Journal of Computational Physics, vol.230, issue.14, pp.5587-5609, 2011. ,
On a well-balanced high-order finite volume scheme for shallow water equations with topography and dry areas, J. Comput. Phys, vol.227, pp.574-601, 2007. ,
Some approximate Godunov schemes to compute shallow-water equations with topography, Computers and Fluids, vol.32, pp.479-513, 2003. ,
A well-balanced flux-vector splitting scheme designed for hyperbolic systems of conservation laws with source terms, Comput. Math. Appl, vol.39, pp.135-159, 2000. ,
A well-balanced scheme for the numerical processing of source terms in hyperbolic equations, SIAM J. Numer. Anal, vol.33, pp.1-16, 1996. ,
An accurate low-Mach scheme for a compressible two-fluid model applied to free-surface flows, Journal of Computational Physics, vol.252, pp.1-19, 2013. ,
DOI : 10.1016/j.jcp.2013.06.008
URL : https://hal.archives-ouvertes.fr/hal-01905434
Numerical simulation of shallow water equations and related models, 2015. ,
URL : https://hal.archives-ouvertes.fr/tel-01216642
Explicit staggered grid scheme for rotating shallow water equations on geostrophic flows, Progress in Computational Fluid Dynamics, vol.18, issue.1, pp.46-55, 2018. ,
DOI : 10.1504/pcfd.2018.10010645
URL : https://doi.org/10.1504/pcfd.2018.10010645
On some implicit and semi-implicit staggered schemes for the shallow water and Euler equations, Mathematical Modelling and Numerical Analysis, vol.48, pp.1807-1857, 2014. ,
DOI : 10.1051/m2an/2014021
URL : https://hal.archives-ouvertes.fr/hal-00805510
Consistent explicit staggered schemes for compressible flows Part i: the barotropic Euler equations, 2013. ,
URL : https://hal.archives-ouvertes.fr/hal-00821069
A steady-state capturing method for hyperbolic systems with geometrical source terms, vol.2, pp.631-645, 2001. ,
DOI : 10.1007/978-1-4613-0017-5_10
URL : http://www.numdam.org/article/M2AN_2001__35_4_631_0.pdf
Well-balanced RKDG2 solutions to the shallow water equations over irregular domains with wetting and drying, Computers and Fluids, vol.39, pp.2040-2050, 2010. ,
DOI : 10.1016/j.compfluid.2010.07.008
Locally limited and fully conserved RKDG2 shallow water solutions with wetting and drying, J. Sci. Comput, vol.50, pp.120-144, 2012. ,
DOI : 10.1007/s10915-011-9476-4
URL : http://eprints.whiterose.ac.uk/79216/8/WRRO_79216.pdf
Central-upwind schemes for the saint-venant system, Mathematical Modelling and Numerical Analysis, vol.36, pp.397-425, 2002. ,
Analysis of Numerically Induced Oscillations in 2D Finite Element Shallow Water Models Part I: Inertia Gravity Waves, SIAM Journal on Scientific Computing, vol.29, issue.1, pp.331-360, 2007. ,
Balancing source terms and flux gradients in high-resolution Godunov methods: the quasisteady wave-propagation algorithm, J. Comput. Phys, vol.146, pp.346-365, 1998. ,
High-order well-balanced central WENO scheme for pre-balanced shallow water equations, Computers & Fluids, vol.99, pp.182-189, 2014. ,
DOI : 10.1016/j.compfluid.2014.04.022
Well-balanced finite volume evolution Galerkin methods for the shallow water equations, J. Comput. Phys, vol.1, pp.122-147, 2007. ,
The NEMO team, NEMO ocean engine, Notes PÃ?le Model, vol.27, 2008. ,
A positivity preserving and well-balanced DG scheme using finite volume subcells in almost dry regions, Applied Mathematics and Computation, vol.272, pp.259-273, 2016. ,
DOI : 10.1016/j.amc.2015.08.121
A well-balanced scheme for the shallow-water equations with topography, Comput. Math. Appl, vol.72, pp.568-593, 2016. ,
URL : https://hal.archives-ouvertes.fr/hal-01513186
Augmented versions of the HLL and HLLC Riemann solvers including source terms in one and two dimensions for shallow flow applications, Journal of Computational Physics, vol.231, pp.6861-6906, 2012. ,
An unstructured node-centered finite volume scheme for shallow water flows with wet/dry fronts over complex topography, Comput. Methods Appl. Mech. Engrg, vol.198, pp.3723-3750, 2009. ,
Well-balanced finite volume schemes of arbitrary order of accuracy for shallow water flows, J. Comput. Phys, vol.213, pp.474-499, 2006. ,
High-order well-balanced finite volume WENO schemes for shallow water equation with moving water, Journal of Computational Physics, vol.226, issue.1, pp.29-58, 2007. ,
Centered-potential regularization of advection upstream splitting method : Application to the multilayer shallow water model in the low Froude number regime, SIAM Journal on Numerical Analysis, vol.54, pp.3083-3104, 2016. ,
Stabilized residual distribution for shallow water simulations, J. Comput. Phys, vol.228, pp.1071-1115, 2009. ,
URL : https://hal.archives-ouvertes.fr/inria-00538892
Central schemes for conservation laws with application to shallow water equations, pp.225-246, 2005. ,
The regional oceanic modeling system (ROMS): a split-explicit, free-surface, topography-following-coordinate oceanic model, Ocean Model, vol.9, pp.347-404, 2005. ,
A projection method-based model with the exact C-property for shallow-water flows over dry and irregular bottom using unstructured finite-volume technique, Computers & Fluids, vol.76, pp.178-195, 2013. ,
URL : https://hal.archives-ouvertes.fr/hal-00947777
An energy and potential enstrophy conserving numerical scheme for the multilayer shallow water equations with complete Coriolis force, Journal of Computational Physics, vol.313, pp.99-120, 2016. ,
Some exact solutions to the nonlinear shallow water wave equations, J. Fluid Mech, vol.107, pp.499-508, 1981. ,
A limiter-based well-balanced discontinuous Galerkin method for shallow-water flows with wetting and drying: One-dimensional case, Advances in Water Resources, vol.85, pp.1-13, 2015. ,
Comparison of unstructured, staggered grid methods for the shallow water equations, Ocean Modelling, vol.28, pp.106-117, 2009. ,
An entropy stable discontinuous Galerkin method for the shallow water equations on curvilinear meshes with wet/dry fronts accelerated by GPUs, J. Compt. Phys, vol.375, pp.447-480, 2018. ,
High order finite difference WENO schemes with the exact conservation property for the shallow water equations, J. Comput. Phys, vol.208, pp.206-227, 2005. ,
A new approach of high order well-balanced finite volume WENO schemes and discontinuous Galerkin methods for a class of hyperbolic systems with source terms, Commun. Comput. Phys, vol.1, pp.100-134, 2006. ,
On the advantage of well-balanced schemes for moving-water equilibria of the shallow water equations, Journal of Scientific Computing, vol.48, pp.339-349, 2011. ,
Positivity-preserving well-balanced discontinuous Galerkin methods for the shallow water equations on unstructured triangular meshes, Journal of Scientific Computing, vol.57, issue.1, pp.19-41, 2013. ,
A well-balanced gas-kinetic scheme for the shallow-water equations with source terms, Journal of Computational Physics, vol.178, pp.533-562, 2002. ,
A well-balanced explicit/semi-implicit finite element scheme for shallow water equations in dryingâ??wetting areas, International Journal for Numerical Methods in Fluids, vol.75, pp.815-834, 2014. ,
The surface gradient method for the treatment of source terms in the shallow-water equations, J. Comput. Phys, vol.168, pp.1-25, 2001. ,