26 citations · 29 across the 5 of their papers we have counts for
6 papers
A fully well-balanced hydrodynamic reconstruction
Christophe Berthon, Victor Michel-Dansac
The present work focuses on the numerical approximation of the weak solutions of the shallow water model over a non-flat topography. In particular, we pay close attention to steady…
A two-dimensional high-order well-balanced scheme for the shallow water equations with topography and Manning friction
Victor Michel-Dansac, Christophe Berthon, Stéphane Clain +1
We develop a two-dimensional high-order numerical scheme that exactly preserves and captures the moving steady states of the shallow water equations with topography or Manning fric…
Numerical Convergence Rate for a Diffusive Limit of Hyperbolic Systems: p-System with Damping
Christophe Berthon, Marianne Bessemoulin-Chatard, Hélène Mathis
This paper deals with diffusive limit of the p-system with damping and its approximation by an Asymptotic Preserving (AP) Finite Volume scheme. Provided the system is endowed with…
An analytical solution of Shallow Water system coupled to Exner equation
Christophe Berthon, Stéphane Cordier, Minh H. Le +1
In this paper, an exact smooth solution for the equations modeling the bedload transport of sediment in Shallow Water is presented. This solution is valid for a large family of sed…
Late-time/stiff relaxation asymptotic-preserving approximations of hyperbolic equations
Christophe Berthon, Philippe G. LeFloch, Rodolphe Turpault
We investigate the late-time asymptotic behavior of solutions to nonlinear hyperbolic systems of conservation laws containing stiff relaxation terms. First, we introduce a Chapman-…
Why many theories of shock waves are necessary. Kinetic relations for nonconservative systems
Christophe Berthon, Frédéric Coquel, Philippe G. LeFloch
For a class of nonconservative hyperbolic systems of partial differential equations endowed with a strictly convex mathematical entropy, we formulate the initial value problem by s…