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Mathieu GIRARDIN

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Ingénieur-Chercheur et titulaire d’un doctorat en Mathématiques Appliquées et Calcul Scientifique, Mathieu Girardin travaille au sein d’une équipe de R&D du CEA dont l’objectif est de développer de nouveaux modèles et de nouvelles méthodes numériques pour les codes de simulation numérique HPC.

Quelques thèmes de recherche

Modélisation, analyse numérique et calcul scientifique autour des systèmes d’équations aux dérivées partielles :

  • Equations hyperboliques non-linéaires
  • Limite Bas-Mach
  • Méthodes Volume finis, schémas explicites et implicites (schéma de relaxation, solver Lagrange-Projection…)
  • Discretization de termes sources (schémas Well-Balanced et Asymptotic-Preserving )
  • Schémas d’ordre élevé(schémas one-step)
  • Turbulence
  • Calcul Scientifique
Second-order schemes based on a relaxation system for scalar and systems of conservation laws
Christophe Chalons   Mathieu Girardin  
Applied Mathematics and Computation, 2025, vol. 490, p. 129173, 2025

abstract

Abstract

In this paper, we propose a new class of second-order one-step time-splitting schemes for scalar and systems of conservation laws. The strategy is based on a relaxation approximation which consists in introducing a relaxation system with linearly degenerate characteristic fields to approximate the original system and deal with its nonlinearities. The numerical schemes are based on the use of arbitrarily high-order approximations of the underlying linear advection equations. Numerical evidence is proposed to illustrate the behaviour of our schemes.

An all-regime Lagrange-Projection like scheme for 2D homogeneous models for two-phase flows on unstructured meshes
Christophe Chalons   Mathieu Girardin   Samuel Kokh  
Journal of Computational Physics, 2017

An All-Regime Lagrange-Projection Like Scheme for the Gas Dynamics Equations on Unstructured Meshes
Christophe Chalons   Mathieu Girardin   Samuel Kokh  
Communications in Computational Physics, 2014

Asymptotic preserving and all-regime Lagrange-Projection like numerical schemes : application to two-phase flows in low mach regime
Mathieu Girardin  
2014

Large Time Step and Asymptotic Preserving Numerical Schemes for the Gas Dynamics Equations with Source Terms
Christophe Chalons   Mathieu Girardin   Samuel Kokh  
SIAM Journal on Scientific Computing, 2013