Professor Iliescu's research is in mathematics of turbulent flows. He creates models, develops algorithms for these models, tests them in realistic settings, and proves theorems that guide practical choices for these models.
His current research focuses on the development of reduced order models (ROMs) for realistic turbulent flows in engineering, geosciences, and medicine. At the core of this research project is the novel idea of using spatial and spectral filtering to model the interactions between resolved and unresolved scales (i.e., closure modeling), which can dramatically increase the ROM accuracy and stability. For all the new ROMs, he proves rigorous error estimates that provide solid mathematical foundations and yield practical scalings for the model parameters.
Another active research area is the construction of computational models for the numerical simulation of ocean flows. These models span a wide range of scales, from thousands of kilometers (e.g., large scale ocean flows that are modeled by the quasi-geostrophic equations) to hundreds of meters (e.g., oceanic gravity currents that are modeled by the Boussinesq equations). Ideas from large eddy simulation (LES) are instrumental in developing novel models that can tackle this staggering scale disparity.