Ensemble modeling of stochastic unsteady open-channel flow in terms of its time-space evolutionary probability distribution: numerical application

Abstract

Abstract. The characteristic form of the Saint-Venant equations was solved in a stochastic setting by using a newly proposed Fokker-Planck Equation (FPE) methodology. This methodology computes the ensemble behavior and variability of a system by directly solving for its time-space evolutionary probability distribution. The new methodology was tested on a 10 stochastic unsteady open-channel flow problem, with an uncertainty arising from the channel's roughness coefficient. The computed statistical descriptions of the flow variables were compared to the results obtained through Monte Carlo (MC) simulations in order to evaluate the performance of the FPE methodology. The comparisons showed that the proposed methodology can adequately predict the results of the considered stochastic flow problem, including the ensemble averages, variances, and probability density functions in time and space. However, unlike the large number of simulations performed 15 by the MC approach, only one simulation was required by the FPE methodology. Moreover, the total simulation period of the FPE methodology was significantly smaller than that of the MC approach. As such, the results obtained in this study indicate that the proposed FPE methodology is a powerful and time-efficient approach for predicting the ensemble average and variance behavior, in both space and time, for an open-channel flow process under an uncertain roughness coefficient.

Ensemble modeling of stochastic unsteady open-channel flow in terms of its time-space evolutionary probability distribution: theoretical development

“…However, the proposed methodology can be expanded to problems which 25 assume uncertainties that arise from other flow or channel parameters. The application and validation of this methodology is provided in a companion paper by Dib and Kavvas (2017), in which the statistical results of the proposed FPE methodology are compared against the results obtained by the MC approach.…”