Free Surface Geophysical Flows
Participants:
E.
Audusse (Univ. Paris Nord),
A.C.Boulanger, M.O. Bristeau, M. Pelanti,
B. Perthame,
J. Sainte-Marie (Laboratoire Saint-Venant, Macs)
We are involved in research concerning the numerical simulation
of free surface geophysical flows such as rivers, lakes, coastal areas.
Many applications related to environmental problems are
concerned :
- Floodings,
- Dam breaks,
- Overland flows on cultivated lands,
- Swelling flows,
- Stratified flows, upwellings,
- Transport and diffusion of pollutants,
- Aquatic ecosystems, photobioreactors.
Modelisation
Different models are considered:
- Saint-Venant Equations (Shallow Water),
Pollutant Transport Equation,
- Multilayer Saint-Venant models,
- Non-hydrostatic extension,
- Navier-Stokes with varying density,
- Rigid lid Navier-Stokes,
- Hydro-biology coupled system.
The derivation of the "shallow water" type models from the Navier-Stokes
system by asymptotic analysis has been studied.
Numerical Methods
The aim is to obtain robust and efficient numerical tools based
on theoretical results ensuring the accuracy and the preservation
of physical properties of the flow (conservation, positivity of
water depth, equilibrium states...). Among others, we have developed:
- Finite Volumes for hyperbolic systems (kinetic scheme, relaxation scheme...)
- Well-balanced schemes,
- Second order schemes.
For most of the considered systems, a kinetic scheme is deduced of a kinetic interpretation
leading to interesting stability results.
Applications
Collaborations
Publications
Français