Mage is a mono dimensional simulating software for river flows. Is is
developed by the CEMAGREF in order to mainly simulate floods. Moreover,
Mage is particularly adapted to simulate flood gates, dams, ... included
in a complex hydraulics network Mage has been created to upgrade the performances
of TALWEG-FLUVIA programs by implementing a solver of transient flows.
Mage is composed of different modules, the entire chain of programs is
as follows:

DONTAL, TALWEG, TALISC, DONFLU, FLUVIA, DONMAG, MAGE, SAISIE. GRAPHE.

In an unsteady flow simulation the different steps are:

1)

- Definition of the geometry
with DONTAL (optional);

- Geometry processing with
the program TALWEG;

- Checking of the results
with TALISC (optional);

2)

- Definition of steady data
with DONFLU (optional);

- Calculation of the steady
free surface with fluvia (optional);

3)

- Adaptation of data for
Mage with DONMAG or modifying directly the different folders with a text
editor;

4)

- Launching of the unsteady
simulation with MAGE;

5)

- Using of SAISIE and GRAPHE
to extract needed information.

Equations are integrated by a half implicit finite differences method . The code is programmed in Fortran-90.

-Mage solves 1D Saint-Venant equations :

Continuity equation:

Dynamic equation:

+ Initial Condition and Boundary Conditions

With t the time, x the abscissa, S the wet section, Z the height of the free surface, V the average velocity, g the gravity, Q the flow, b the quantity of movement coefficient J the linear loss flow rate, Js the singular loss flow rate and q the lateral losses or supplies.

- The network can be as complex as we want. It can be meshed, it is to say that there are defluences, or ramified (only confluence's).

- Upstream boundary conditions are given by variable flows. We can also ad a lateral flow at any node which has not a downstream condition. Few rules must be respected. We can not have a defluence at the level of an upstream boundary condition: boundary conditions are affected to reaches and we must have a reach for each upstream boundary condition.

- Downstream conditions can be two different kind:

* a level variable with time,
we give a limnigram Z(t)

* we give a flow law Q(t)

As for the upstream conditions we can not have a confluence at the level of a downstream boundary condition : boundary conditions are affected to reaches and we must have a reach for each downstream boundary condition.

- It is supposed there is no loss flow rate at the nodes. Consequently, the level of the surface in the section of each reach which arrives at the node is the same of the ones of upstream sections from each reach running away the node. Moreover we there is the preservation of the volumes at the nodes.

- Mage is able to simulate the overflowing of a river in the average bed and/or in the greatest bed. More accurately, during a flood we can observe in a transverse section 3 different beds in which the level of surface is the same:

* the minor bed where there
is always water;

* the average bed where
there is a flow only when a certain level is reached;

* the major bed of storage
which fills with water only after a higher level.

** We can see on this photograph that the river has reached
the major bed during this flood.**

We admit velocities can be neglected in this last part of the bed. Consequently, we only consider the storage effects.

- Mage can take into account two sorts of singularities:

* sudden widening or narrowing of the river section can be simulated by a singular loss flow rate. These singularities are automatically noticed by Mage.

* hydraulics works which stop the normal flow and do not respect the Saint-Venant equations. This type of singularity must be defined by the user. Presently are available:

- overflows ( with variable opening laws)

- gates ( with variable opening laws)

- valves

- pumps

- lateral overflows

- circular ducts

- The initial condition can be a steady free surface calculated with FLUVIA or an unsteady free surface calculated before by MAGE.

- Mage is incapable of simulating passages to torrential (Froude > 1). However, if such a changing is due to a sudden geometry variation of the reach we will be able to simulate it inserting a step, that is to say a singular section a the level of the geometry singularity.

- Mage can not take into account loss flow rate at the nodes. More particularly we can not consider the angle of a confluence or a defluence.

- Mage can not simulate really dry reach.

-Mage versus FLUVIA

Both Mage and FLUVIA have been developed by the CEMAGREF. Mage is an upgrated version of FLUVIA. On the one hand, Mage enables to simulate transient flows whereas FLUVIA is limited to steady flows. On the other hand, Mage has a graphical interface which makes its use easier contrary to FLUVIA whose data capture is done in a DOS window.

-Mage versus TELEMAC

The main difference between Mage and TELEMAC is that Mage is a mono
dimensional solver while TELEMAC can solve 2D problems. Consequently, Mage
is able to simulate a flow all along a river and TELEMAC is capable of
calculating the 2D flow in a confined area (about few km2). Moreover, TELEMAC
is able to simulate the passage to torrential flow whereas it is not possible
with Mage.

Another point is that the use of TELEMAC requires a mesher Matisse
and a post-processor Rubens while the graphical interface of Mage gathers
these three steps.