Research interests

Numerical methods to approximate hyperbolic systems of PDE

• Methods
  • Finite Volume methods
  • MUSCL Reconstruction in 1D and 2D
  • A posteriori limitation methods like MOOD
  • Eelaxation methods
• Properties of the schemes
  • Robustness: Preservation of the set of physical admissible states
  • Entropic stability
  • High-order methods
  • Preservation of steady states
  • Optimization of the CFL restriction and reduction of the CPU time
• Applications
  • Compressible fluid dynamics : Euler equations with or without ravity terms
  • Shallow-water flows: with or without temperature gradient
  • Blood flows in arteries: 1D model

Data assimilation methods for an inverse problem coming from transport of pollutants

• Weighted methods
• Parcimonious methods (Orthogonal Matching Pursuit, Iterative Soft Thresholding)