Automatic sensitivity analysis of a finite volume model for two-dimensionnal shallow water flows

O. Souhar (1) , J.B. Faure (1) , André Paquier (1)

1 UR HHLY - Hydrologie-Hydraulique

Given a numerical model for solving two-dimensional Shallow Water Equations, we are interested in the robustness of the simulation by identifying the rate of change of the water depths and discharges with respect to a change in the bottom friction coefficients. Such a sensitivity analysis can be carried out by computing the corresponding derivatives. Automatic Differentiation (AD) is an effcient numerical method, free of approximation errors, to evaluate derivatives of the objective function specified by the computer program, Rubar20 for example. In this paper AD software tool Tapenade is used to compute forward derivatives. Numerical tests were done to show the robustness of the model and to demonstrate the effciency of these AD-derivatives.

Mots clés: EQUATION DE SAINT VENANT; ECOULEMENT; MODELE NUMERIQUE; SIMULATION NUMERIQUE; INCERTITUDE; MODELE HYDRAULIQUE; SENSIBILITE; DIFFERENCIATION; MODELE BIDIMENSIONNEL; SHALLOW WATER EQUATIONS; SENSITIVITY ANALYSIS; UNCERTAINTY PROPAGATION; AUTOMATIC DIFFERENTIATION; HYDRAULIC MODEL

Domaines: Sciences de l'environnement

O. Souhar, J.B. Faure, André Paquier. Automatic sensitivity analysis of a finite volume model for two-dimensionnal shallow water flows. Environmental Fluid Mechanics, 2007, 7, p. 303 - p. 315. ⟨10.1007/s10652-007-9028-5⟩. ⟨hal-00453843⟩