Articles | Volume 22, issue 3
Research article
28 Mar 2018
Research article |  | 28 Mar 2018

Ensemble modeling of stochastic unsteady open-channel flow in terms of its time–space evolutionary probability distribution – Part 2: numerical application

Alain Dib and M. Levent Kavvas

Abstract. The characteristic form of the Saint-Venant equations is solved in a stochastic setting by using a newly proposed Fokker–Planck Equation (FPE) methodology. This methodology computes the ensemble behavior and variability of the unsteady flow in open channels by directly solving for the flow variables' time–space evolutionary probability distribution. The new methodology is tested on a stochastic unsteady open-channel flow problem, with an uncertainty arising from the channel's roughness coefficient. The computed statistical descriptions of the flow variables are compared to the results obtained through Monte Carlo (MC) simulations in order to evaluate the performance of the FPE methodology. The comparisons show 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. Unlike the large number of simulations performed by the MC approach, only one simulation is required by the FPE methodology. Moreover, the total computational time of the FPE methodology is smaller than that of the MC approach, which could prove to be a particularly crucial advantage in systems with a large number of uncertain parameters. 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.

Short summary
A newly proposed method is applied to solve a stochastic unsteady open-channel flow system (with an uncertain roughness coefficient) in only one simulation. After comparing its results to those of the Monte Carlo simulations, the new method was found to adequately predict the temporal and spatial evolution of the probability density of the flow variables of the system. This revealed the effectiveness, strength, and time efficiency of this new method as compared to other popular approaches.