Uncertainty analysis of open channel flow: Stochastic approach to advection-diffusion equation

In fluid mechanics applications, transport occurs through the combination of advection and diffusion. This paper presents a stochastic approach to describe uncertainty and its propagation based on Advection-Diffusion Equation. To assess the uncertainty in initial water depth, random initial condition is imposed on the framework of ID open cannel flow. Karhunen-Loeve Expansion is adopted to decompose the uncertain parameter in terms of infinite series containing a set of orthogonal Gaussian random variables. Eigenstructures of covariance function associated with the random parameter, which play a key role in computing coefficients of the series, are extracted from Fredhulm s equation. The flow depth is also represented as an infinite series of its moments, obtained via polynomial expansion decomposition in terms of the products of random variables. Coefficients of these series are obtained by a set of recursive equations derived from the ADE. Results highlight the effect of various statistical properties of initial water depth. The mean value and variance for the flow depth are compared with Monte Carlo Simulation as a reliable stochastic approach. It is found that when higher-order approximations are used, KLE results would be as accurate as the results of MCS, however, with much less computational time and effort.