94 citations · 439 across the 45 of their papers we have counts for
47 papers
Novel well-balanced continuous interior penalty stabilizations
Lorenzo Micalizzi, Mario Ricchiuto, Rémi Abgrall
In this work, the high order accuracy and the well-balanced (WB) properties of some novel continuous interior penalty (CIP) stabilizations for the Shallow Water (SW) equations are…
A personal discussion on conservation, and how to formulate it
Remi Abgrall
Since the celebrated theorem of Lax and Wendroff, we know a necessary condition that any numerical scheme for hyperbolic problem should satisfy: it should be written in flux form.…
An arbitrarily high order and asymptotic preserving kinetic scheme in compressible fluid dynamic
Rémi Abgrall, Fatemeh Nassajian Mojarrad
We present a class of arbitrarily high order fully explicit kinetic numerical methods in compressible fluid dynamics, both in time and space, which include the relaxation schemes b…
A New Approach for Designing Well-Balanced Schemes for the Shallow Water Equations: A Combination of Conservative and Primitive Formulations
Remi Abgrall, Yongle Liu
In this paper, we introduce a new approach for constructing robust well-balanced numerical methods for the one-dimensional Saint-Venant system with and without the Manning friction…
A Monte-Carlo ab-initio algorithm for the multiscale simulation of compressible multiphase flows
Marco Petrella, Remi Abgrall, Siddhartha Mishra
We propose a novel Monte-Carlo based ab-initio algorithm for directly computing the statistics for quantities of interest in an immiscible two-phase compressible flow. Our algorith…
\textit{A Posteriori} local subcell correction of high-order discontinuous Galerkin scheme for conservation laws on two-dimensional unstructured grids
François Vilar, Rémi Abgrall
We present the two-dimensional unstructured grids extension of the a posteriori local subcell correction of discontinuous Galerkin (DG) schemes introduced in [52]. The technique is…