Quelques aspects de l'emploi des modèles mathématiques fluviaux

Some aspects of the use of mathematical river models

¹ Ingénieur E.I.H. (SO.GR.E.A.H.).
² Docteur ès Sciences (SO.GH.E.A.H.).

Résumé

Basic equations : A mathematical river model relies on two equations with a very simple physical meaning. These are : (i) The continuity equation expressing conservation of the volume of water ; (ii) The dynamic equation expressing equilibrium of gravity, friction and inertia forces. These equations take different special forms for dams, weirs, or set boundary conditions. Numerical methods : As there is generally no analytical solution available for equations defining flow, one has to rely on finite difference procedure. Computers are particularly well suited for such methods. Data required and the construction of a model : As for any other model, the value of a mathematical model depends on that of its topographical and hydraulic data. The latter data can be adjusted under unsteady flow conditions on the strengh of observed floods, which is a great advantage. The comparison phase between model and real life conditions frequently amounts to a comprehensive analysis method for the hydraulic behaviour of the considered river. Applications : Mathematical river models are eminently suitable for overall river basin problems, such as the following: Natural flood formation and propagation from tributary flows ; Modifications expected by dyking or other large-scale correction works ; Study of flow conditions due to control operations at dams. A particular advantage of the method is the ease with which it enables several alternative versions of a project to be studied with a view to comparing their respective effects.