Simulation unidimensionnelle de l’écoulement à surface libre avec un schéma numérique TVD en discrétisation implicite et explicite

One Dimensional Free Surface flow Simulation by Means of a TVD numerical scheme with an Implicit and an Explicit Time Integrations

¹ U.P.R. Systèmes Hydrauliques Urbains, Ecole Nationale du Génie de l’Eau et de l’Environnement de Strasbourg 1 quai Koch BP 1039 F, 67070 STRASBOURG cedex, France
² Institut National des Sciences Appliqués de Strasbourg 24 boulevard de la Victoire, 67084 STRASBOURG cedex, France

Auteur de correspondance : georges.kesserwani@engees.u-strasbg.fr

Abstract

When simulating the shallow water equations. A question to ask: what type of temporal discretization “implicit or explicit” is more suitable according to the nature of the hydraulic problem? In this paper, a Total Variation Diminishing (TVD) scheme is considered based on fully explicit and fully implicit time discretization, respectively. The aim is to simulate the open channel flow with steady and transient tests. Numerical results have been evaluated via analytical solutions. The error between the analytical and numerical solution, and the CPU time cost are investigated in order to conclude the advantage and the disadvantage of the implicit scheme with respect to the explicit in the simulation of steady and transient water flow. For the steady test, the fully implicit scheme leads to stable and accurate solutions, presented using CFL values up to 2000. On the other hand, the fully explicit scheme appears to be more suitable for the transient test.