1-Definition of the mesh and boundary conditions 1.1-Bathymetry of the domain

Using the file  ".geo" that we have create with the software Matisse, we manage to display the bathymetry with the software Rubens : 1.2-Meshing of the domain

The software Matisse allows , using the bathymetrics information, to create a mesh constituted of triangular elements.
the two following graphs show in the first case the whole domain and the second case a zoom on this domain  fig 1 zoom on a zone of the  "mesh1"

In fact, we used two different mesh and got results for each one. The mesh on the figure 1 is constituted of 3940  nodes (we call it "mesh1") and the second one is build up with 8401 nodes ("mesh2").  fig 2 :  zoom on a zone of the  "mesh2"

1.3-Boundary conditions

We decided to impose the following boundaries conditions :

•       flow rate imposed for the inlet flow
•       flow rate imposed the two lateral boundary
•       Outflow condition for the outlet condition
For the "mesh2",   the outlet condition impose that the sum of the incoming flow into the domain (inlet flow + lateral flow) is equal to the outgoing flow. Hence the imposed outflow is constant and equal to 3000 m3/s.
For the "mesh1", we use the file "Q.f" to compute with the Strickler law a flow rate that depends on the water height: 1.4-Initialization of the problem

In the first case, we imposed an "empty" domain which is filled when the simulation goes on. In order to fasten the calculation, we decided not to use the "Banc decouvrant" option that permits a null water height in the domain. Hence we imposed a water height of 1 centimetre as an initialization of the problem, in this case we can simulate the fulfilment of the valley without increasing the calculation time.
In the second case, as we imposed a constant outflow, we needed to initialize the problem not too far from the solution. Indeed if the initialization is too far from the physical solution, like an empty domain for example, will lead to a solution that isn't physical, in the previous example it will lead to very high water speed and not to a fulfilment of the valley. Hence, we decided to initiate the problem with a water height of 2 meters which is near enough from the physical solution to lead to it.