Axelle DROUARD
Axelle DROUARD is currently a PhD student at CEA, supervised by Stephane Del Pino, Engineer Researcher at CEA. Her thesis director is Emmanuel Labourasse, HDR Engineer Researcher at CEA and her co-director is Remi Abgrall, Professor at the Institute of Mathematics of the University of Zurich. Axelle’s thesis topic is the following: « Semi-implicit numerical method for the hyper-elasticity model ». The goal of this thesis is to design, analyze and implement a numerical method for the hyper-elasticity system, and to extend it in dimensions higher than one on unstructured meshes.
Computers & Fluids, Volume 297, 106648, 2025
abstract
Abstract
In this paper, we present an extension to non-uniform meshes of a 1D scheme [Rémi Abgrall and Davide Torlo. “Some preliminary results on a high order asymptotic preserving computationally explicit kinetic scheme”. In: Abgrall and Torlo (2022). This scheme is arbitrary high order convergent in space and time for any hyperbolic system of conservation laws. It is based on a Finite Difference technique. We show that this numerical method is not conservative but it satisfies a Lax–Wendroff theorem under restrictive conditions on the mesh. To relax this condition we propose a Finite Volume alternative. This new discretization can be seen as a direct generalization to non-uniform meshes of the Finite Difference schemes in the sense that the fluxes of both methods are the same on uniform meshes. We apply the two schemes to the Euler system and we assess their performances on regarding test problems of the literature.