[LAMPS] Besoins en mathématiques dans l’étude de l’épigénome et son impact évolutif

Résumé

This presentation focuses on two complementary aspects of numerical analysis in fluid mechanics : high-fidelity simulation of turbulent natural convection and data analysis of complex flow dynamics.
First, we investigate heat transfer in a differentially heated cavity with an aspect ratio of 1/4, where the horizontal walls are modeled using conjugate heat transfer. Direct numerical simulations are performed at a Rayleigh number of 2x10⁹ using a spectral collocation method and an influence-matrix method to ensure the continuity between solid and fluid.
The numerical approach is validated with a turbulent natural-convection benchmark in the case of adiabatic-walls.
Then, we explore dimension reduction techniques for the analysis technics for the analysis of multidimensional time-dependent data obtained from simulations. In particular, Principal Components Analysis in the Frequency Domain (PCAFD), newly applied in this context, is compared with Proper Orthogonal Decomposition and Spectral Proper Orthogonal Decomposition. The discussion shows that PCAFD can be used to identify the physical mechanisms in complex flows.
 

Intervenant