A relaxation method for two-phase flow models with hydrodynamic closure law. - Michael Baudin; Christophe Berthon; Frédéric Coquel; Roland Masson; Quang-Huy Tran (Numerische Mathematik, 2005)

Robustness of MUSCL schemes for 2D unstructured meshes. - Christophe Berthon (J. Comput. Phys., 2006)

Numerical approximations of the 10-moment Gaussian closure. - Christophe Berthon (Math. Comput., 2006)

Why the MUSCL-Hancock Scheme is L1-stable. - Christophe Berthon (Numerische Mathematik, 2006)

An HLLC Scheme to Solve The M 1 Model of Radiative Transfer in Two Space Dimensions. - Christophe Berthon; Pierre Charrier; Bruno Dubroca (J. Sci. Comput., 2007)

Nonlinear projection methods for multi-entropies Navier-Stokes systems. - Christophe Berthon; Frédéric Coquel (Math. Comput., 2007)

A Positive Preserving High Order VFRoe Scheme for Shallow Water Equations: A Class of Relaxation Schemes. - Christophe Berthon; Fabien Marche (SIAM J. Sci. Comput., 2008)

Preface. - Rémi Abgrall; Denise Aregba; Christophe Berthon; Manuel J. Castro; Carlos Parés (J. Sci. Comput., 2011)

Efficient well-balanced hydrostatic upwind schemes for shallow-water equations. - Christophe Berthon; Françoise Foucher (J. Comput. Phys., 2012)

A Local Entropy Minimum Principle for Deriving Entropy Preserving Schemes. - Christophe Berthon; Bruno Dubroca; Afeintou Sangam (SIAM J. Numer. Anal., 2012)

Space-time Generalized Riemann Problem Solvers of Order k for Linear Advection with Unrestricted Time Step. - Christophe Berthon; Céline Sarazin; Rodolphe Turpault (J. Sci. Comput., 2013)

Late-time/stiff-relaxation asymptotic-preserving approximations of hyperbolic equations. - Christophe Berthon; Philippe G. LeFloch; Rodolphe Turpault (Math. Comput., 2013)

Asymptotic preserving scheme for the shallow water equations with source terms on unstructured meshes. - Arnaud Duran; Fabien Marche; Rodolphe Turpault; Christophe Berthon (J. Comput. Phys., 2015)

A well-balanced scheme for the shallow-water equations with topography. - Victor Michel-Dansac; Christophe Berthon; Stéphane Clain; Françoise Foucher (Comput. Math. Appl., 2016)

A Well-Balanced Finite Volume Scheme for a Mixed Hyperbolic/Parabolic System to Model Chemotaxis. - Christophe Berthon; Anaïs Crestetto; Françoise Foucher (J. Sci. Comput., 2016)

A fully well-balanced, positive and entropy-satisfying Godunov-type method for the shallow-water equations. - Christophe Berthon; Christophe Chalons (Math. Comput., 2016)

Well-balanced schemes to capture non-explicit steady states: Ripa model. - Vivien Desveaux; Markus Zenk; Christophe Berthon; Christian Klingenberg (Math. Comput., 2016)

A well-balanced scheme for the shallow-water equations with topography or Manning friction. - Victor Michel-Dansac; Christophe Berthon; Stéphane Clain; Françoise Foucher (J. Comput. Phys., 2017)

A simple fully well-balanced and entropy preserving scheme for the shallow-water equations. - Christophe Berthon; Victor Michel-Dansac (Appl. Math. Lett., 2018)

Improvement of the Hydrostatic Reconstruction Scheme to Get Fully Discrete Entropy Inequalities. - Christophe Berthon; Arnaud Duran; Françoise Foucher; Khaled Saleh; Jean de Dieu Zabsonré (J. Sci. Comput., 2019)

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; Françoise Foucher (CoRR, 2020)

A fully well-balanced scheme for the 1D blood flow equations with friction source term. - Beatrice Ghitti; Christophe Berthon; Minh Hoang Le; Eleuterio F. Toro (J. Comput. Phys., 2020)

A stable fixed point method for the numerical simulation of a kinetic collisional sheath. - Mehdi Badsi; Christophe Berthon; Anaïs Crestetto (J. Comput. Phys., 2021)

Design of coupled finite volume schemes minimizing the grid orientation effect in reservoir simulation. - Karine Laurent; Eric Flauraud; Christophe Preux; Quang-Huy Tran; Christophe Berthon (J. Comput. Phys., 2021)

A Very Easy High-Order Well-Balanced Reconstruction for Hyperbolic Systems with Source Terms. - Christophe Berthon; Solène Bulteau; Françoise Foucher; Meissa M'Baye; Victor Michel-Dansac (SIAM J. Sci. Comput., 2022)

Artificial Viscosity to Get Both Robustness and Discrete Entropy Inequalities. - Christophe Berthon; Manuel Jesús Castro Díaz; Arnaud Duran; Tomás Morales de Luna; Khaled Saleh (J. Sci. Comput., 2023)

An entropy-stable and fully well-balanced scheme for the Euler equations with gravity. - Christophe Berthon; Victor Michel-Dansac; Andrea Thomann (CoRR, 2024)

A fully well-balanced hydrodynamic reconstruction. - Christophe Berthon; Victor Michel-Dansac (J. Num. Math., 2024)