Modeling and numerical methods for hydraulics and environmental processes

Description:
This course is dedicated to the modeling of free-surface flows on large time and space scales, and to their resolution using appropriate numerical methods. Both surface flows (rivers, lakes, oceans) and subsurface flows (groundwater) will be covered, using numerical experimentation.
Course outline:

Single-layer Saint-Venant model ("shallow water"). This model is the cornerstone of geophysical models and is widely used for land-use planning (dams, bridges, dikes), flood forecasting and flood risk management.
Multi-layer Saint-Venant model. We'll be looking at how to overcome some of the shortcomings of the single-layer model by proposing a version that takes better account of boundary layers for improved reproduction of friction processes and wind forcing.
Boussinesq model. We will see how to take into account the dispersive effects necessary for wave propagation and submergence waves.
Richards model. We study subsurface flow in saturated and unsaturated porous media. The Richards model provides a rich representation of infiltration processes for applications in soil pollution and water quality.
Dupuit-Forchheimer model. This focuses on groundwater level estimation for applications such as groundwater pumping, saltwater intrusion and geothermal energy.
Numerical experimentation of the models will also be covered in parallel with the model introduction.

Organization:
Sessions are organized in blocks of 4h (typical course: 2h of CM/TD followed by 2h of applicative TP).
assessment:
The module will be assessed on the work carried out in TP (1/3) and on the realization of a project (2/3). The make-up session will consist in writing a report on a subject proposed by the teacher.

Fluid mechanics I and II
Physics of free-surface flows
Numerical methods for transport equations

Fluid and energetic