5 citations · 5 across the 9 of their papers we have counts for
9 papers
On structure-preserving and pointwise conservative continuous DG schemes for hyperbolic systems
Rémi Abgrall, Michael Dumbser, Pierre-Henri Maire +1
We present a new class of structure-preserving semi-discrete continuous-discontinuous Galerkin (CG-DG) finite element schemes for linear and nonlinear hyperbolic systems of partial…
Embedding General Conservation Constraints in Discretizations of Hyperbolic Systems on Arbitrary Meshes: A Multidimensional Framework
Rémi Abgrall, Pierre-Henri Maire, Mario Ricchiuto
The purpose of this review is to discuss the notion of conservation in hyperbolic systems and how one can formulate it at the discrete level depending on the solution representatio…
Dual Formulation Finite-Volume Methods on Overlapping Meshes for Hyperbolic Conservation Laws
Rémi Abgrall, Alina Chertock, Alexander Kurganov +1
In this work, we introduce new second-order schemes for one- and two-dimensional hyperbolic systems of conservation laws. Following an approach recently proposed in [{\sc R. Abgral…
An Explicit Primitive Conservative Solver for the Euler Equations with Arbitrary Equation of State
Giuseppe Sirianni, Alberto Guardone, Barbara Re +1
This work presents a procedure to solve the Euler equations by explicitly updating, in a conservative manner, a generic thermodynamic variable such as temperature, pressure or entr…
A new local and explicit kinetic method for linear and non-linear convection-diffusion problems with finite kinetic speeds: II. Multi-dimensional case
Gauthier Wissocq, Rémi Abgrall
We extend to multi-dimensions the work of [1], where new fully explicit kinetic methods were built for the approximation of linear and non-linear convection-diffusion problems. The…
Active flux for triangular meshes for compressible flows problems
Rémi Abgrall, Jianfang Lin, Yongle Liu
In this article, we show how to construct a numerical method for solving hyperbolic problems, whether linear or nonlinear, using a continuous representation of the variables and th…
A new local and explicit kinetic method for linear and non-linear convection-diffusion problems with finite kinetic speeds: I. One-dimensional case
Gauthier Wissocq, Rémi Abgrall
We propose a numerical approach, of the BGK kinetic type, that is able to approximate with a given, but arbitrary, order of accuracy the solution of linear and non-linear convectio…
A semi-discrete Active Flux method for the Euler equations on Cartesian grids
Rémi Abgrall, Wasilij Barsukow, Christian Klingenberg
Active Flux is an extension of the Finite Volume method and additionally incorporates point values located at cell boundaries. This gives rise to a globally continuous approximatio…
Robust Model Reduction Of Hyperbolic Problems by -norm Minimization and Dictionary Approximation
Remi Abgrall, David Amsallem, Roxana Crisonovan
We propose a novel model reduction approach for the approximation of non linear hyperbolic equations in the scalar and the system cases. The approach relies on an offline computati…