Non-permanent free surface flows - 5EMHAAG0

Goal(s)

Understand the physics and the modeling of unsteady flows in the rivers and canals (propagation of the tide, floods and of rapidly varying flows in the rivers and canals). Saint Venant equation formulation.
Design the volume of retention dams for flood protection.
Understanding the links between the physical reality, its perception and its modeling.
Brief presentation of the market software properties dealing with this problem.

Content(s)

1.- Introduction on the floods and floodings. Relinders on open channel hydraulics Hydraulics.
2.- One-dimensional free surface flows: the Barré de Saint-Venant PDE equations. Physical meaning of the different terms of the equations. Mathematical properties: the characteristics and the invariants.
3.- Physics of floods and their modeling. Kinematic and diffusive approximation. Example: the deterministic runoff.
4.- 1D numerical modeling of the equations: Preissman implicit scheme. Discretization, stability and quality of the numerical scheme. Initial conditions and limit conditions. Propagation celerity of a perturbation. 1D reduction of the reality: wire and rack model. Geometrical singularities: pressure drop particular to the works, confluences and distributaries.
5.- Flood alleviating structures: physical principles and optimisation of dams by a costs-benefits analysis
6.- Rapidly varying unsteady open channel flows dominates by inertia: shock and rarefaction waves. Sudden stop of a flow and dam breakage.

• Steady open channel flow hydraulics
• Hyperbolic partial differential equations (characteristics)
• Statistics