Modelling, analysis and simulation of geophysical flows are complex and challenging topics upon applied research and engineering. The growing importance of sustainable development issues coupled with the complexity of the aforementioned problems imply to go further than the classic shallow water equations. The issues investigated within the team mainly concern gravity driven flows such as hazardous flows (flooding, rogue waves, landslides, …), sustainable energies (hydrodynamics-biology coupling, biofuel production, marine energies, …), risk management and land-use planning (morphodynamic evolutions, early warning systems, …).
The research programme of ANGE consists in deriving and analysing models (PDE) of reduced complexity with respect to the Navier-Stokes equations and enriched with respect to the classic shallow water system. This process provides a hierarchy of models mainly of hyperbolic type (conservation laws). Our core activity is split into three components, that are briefly described in the sequel:
- Modelling: The standard shallow water equations have been the cornerstone of flow modelling in geosciences. We now intend to derive models that more accurately approximate the Euler or the Navier-Stokes equations.
- Mathematical and numerical analysis: The rigorous derivation of a model is not sufficient to ensure a good mathematical structure. Existence, uniqueness, positivity, monotonicity, energy estimates, etc. are crucial properties that reinforce the legitimacy of those models. Numerical schemes must then account for those properties to lead to accurate and relevant solutions. Numerical analysis is a strong point of the team.
- Scientific computing and data processing: Besides the publication of our results in journals of applied mathematics, our objective is also to have a strong impact over the geosciences community by the dissemination of results and numerical tools (subroutines, softwares, …). Industrial contracts and collaborations with geophysicists and biologists are also an indicator of the scientific achievements.
ANGE was formerly (2013-2018) a joint team with CEREMA (Center for Research on Hazards, Environment, Mobility and Layout – Ministry of transition for ecology and solidarity).
Team Project Leader
Sorbonne Université, Laboratoire Jacques-Louis Lions