25 citations · 66 across the 11 of their papers we have counts for
11 papers
High order asymptotic preserving scheme for linear kinetic equations with diffusive scaling
Megala Anandan, Benjamin Boutin, Nicolas Crouseilles
In this work, high order asymptotic preserving schemes are constructed and analysed for kinetic equations under a diffusive scaling. The framework enables to consider different cas…
Stability of finite difference schemes for the hyperbolic initial boundary value problem by winding number computations
Benjamin Boutin, Pierre Le Barbenchon, Nicolas Seguin
In this paper, we present a numerical strategy to check the strong stability (or GKS-stability) of one-step explicit finite difference schemes for the one-dimensional advection equ…
On the stability of totally upwind schemes for the hyperbolic initial boundary value problem
Benjamin Boutin, Pierre Le Barbenchon, Nicolas Seguin
In this paper, we present a numerical strategy to check the strong stability (or GKS-stability) of one-step explicit totally upwind schemes in 1D with numerical boundary conditions…
Coupling techniques for nonlinear hyperbolic equations. II. Resonant interfaces with internal structure
Benjamin Boutin, Frédéric Coquel, Philippe G. LeFloch
In the first part of this series, an augmented PDE system was introduced in order to couple two nonlinear hyperbolic equations together. This formulation allowed the authors, based…
High order numerical schemes for transport equations on bounded domains
Benjamin Boutin, Thi Hoai Thuong Nguyen, Abraham Sylla +2
This article is an account of the NABUCO project achieved during the summer camp CEMRACS 2019 devoted to geophysical fluids and gravity flows. The goal is to construct finite diffe…
Some remarks about flows of Hilbert-Schmidt operators
Benjamin Boutin, Nicolas Raymond
This paper deals with bracket flows of Hilbert-Schmidt operators. We establish elementary convergence results for such flows and discuss some of their consequences.
Stability of finite difference schemes for hyperbolic initial boundary value problems: numerical boundary layers
Benjamin Boutin, Jean-François Coulombel
In this article, we give a unified theory for constructing boundary layer expansions for dis-cretized transport equations with homogeneous Dirichlet boundary conditions. We exhibit…
Coupling techniques for nonlinear hyperbolic equations. IV. Multi-component coupling and multidimensional well-balanced schemes
Benjamin Boutin, Frédéric Coquel, Philippe G. LeFloch
This series of papers is devoted to the formulation and the approximation of coupling problems for nonlinear hyperbolic equations. The coupling across an interface in the physical…
Coupling techniques for nonlinear hyperbolic equations. III. The well-balanced approximation of thick interfaces
Benjamin Boutin, Frédéric Coquel, Philippe G. LeFloch
We continue our analysis of the coupling between nonlinear hyperbolic problems across possibly resonant interfaces. In the first two parts of this series, we introduced a new frame…
Coupling techniques for nonlinear hyperbolic equations. I. Self-similar diffusion for thin interfaces
Benjamin Boutin, Frédéric Coquel, Philippe G. LeFloch
We investigate various analytical and numerical techniques for the coupling of nonlinear hyperbolic systems and, in particular, we introduce here an augmented formulation which all…
Convergent and conservative schemes for nonclassical solutions based on kinetic relations
Benjamin Boutin, Christophe Chalons, Frederic Lagoutiere +1
We propose a new numerical approach to compute nonclassical solutions to hyperbolic conservation laws. The class of finite difference schemes presented here is fully conservative a…