Mathieu GIRARDIN
Mathieu Girardin is a Research Engineer and holds a PhD in Mathematics Applied to Scientific Computing. He is currently member of an R&D team at CEA whose objective is to develop new models and new numerical methods for HPC numerical simulation codes.
Some research topics
Modelization, numerical analysis and scientific computation around partial differential equations and systems of conservating laws :
- Nonlinear hyperbolic equations
- Low-Mach number limit
- Finite Volume Methods, explicit and implicit schemes (relaxation schemes, Lagrange-Remap solvers, …)
- Discretization of sources (Well-Balanced and Asymptotic-Preserving schemes)
- High-order schemes(one-step schemes)
- Turbulent flows
- Scientific computing
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.
Journal of Computational Physics, 2017
Communications in Computational Physics, 2014
2014
SIAM Journal on Scientific Computing, 2013