**Introduction**

The objective of the present BES is computation of free surface flow in a horizontal canal with a hump in the middle. This will be lead using Telemac2d's software. It is a module of the Telemac systeme , a computational code largely used in industry. The Telemac 2d module is based on the famous Saint Venant equqtions for non linear long waves.

In this work we will pay a special attention to boundary conditions under different flow regims.

We will eventually use an other module (TSEF) wich will allow us to study the sedimentation in the bottom of the canal.

**Remind : Saint Venant Equations.**

Saint-Venant equations is a systeme of non linear equations. Its the result of the long wave aproximation. This approximation is handeled in problems where the depth is neglected if we compare it to the length of the surface waves. This lead to an hyperbolic systeme, with three variables H ,U and V, respectively water height, longitudinal velocity and transversal one. The solution of this systeme are two waves moving with different velocities. The sign of these velocities depend on the Froud number.

We will reduce our study to the only one dimentional problem in wich only two variables subsist. even if we are studying a simple systeme it will allow us to test the code and verify theory in a large scale.