Un nouvel algorithme pour une solution robuste des équations complètes de Saint-Venant

Abstract

A new procedure for the numerical solution of the fully dynamic shallow water equations is presented. The procedure is a fractional step methodology where the original system is split into two sequential ones. The first system differs from the original one because of the head gradient term, that is treated as constant and equal to the value computed at the end of the previous time step. The solution of this system, called kinematic, is computed in each element using a spatial zero order approximation for both the heads and the flow rates by means of integration of single ODEs. The second system is called diffusive, contains in the momentum equations only the complementary terms and can be easily solved using implicit methods. The major advantages of the methodology are: (1) it guarantees mass conservation; (2) it shows unconditional stability with respect to the Courant number; (3) it can be applied to initially dry domains; (4) it can be applied to closed conduits without the help of the Preissman approximation.