Approach for uncertainty propagation and design in Saint Venant equations via automatic sensitive derivatives applied to Saar river
Étude de la propagation des incertitudes dans les équations de Saint-Venant à l'aide de la Différenciation Automatique. Application à la rivière Saar
Résumé
This paper describes the assessment of uncertainties of Computational Fluid Dynamics (CFD) for modelling free surface flows. A series of CFD simulations, using MAGE, are employed to compute flood extent resulting from the overflow of rivers. These simulated outputs are affected by uncertainties in the empiric roughness coefficients. Uncertainty propagation in MAGE outputs is difficult to evaluate because of the complexity and the nonlinearity of models. Assessment of uncertainties may be carried out by computing derivatives of the output results with respect to the inputs. Recently, Automatic Differentiation (AD) has become an efficient numerical method for sensitivity analysis and assessment of uncertainties. In this paper, AD is used to transform mechanically a given one-dimensional hydraulic model, MAGE, into a new program capable of computing the original simulation and the desired derivatives. Specifically, derivatives of the flood extent and water width with respect to the roughness coefficients are computed. Numerical experiments of derivatives obtained from AD and Divided Difference (DD) approximations are compared, validating derivatives obtained by AD. Results can serve to evaluate existing flood models.