Stochastic Partial Differential Equation-Based Model for Suspended Sediment Transport in Surface Water Flows

Abstract

A stochastic partial differential equation-based model has been derived based on the law of mass conservation and the Langevin equation of particle displacement to simulate suspended sediment transport in open-channel flows. In this model, the movement of any suspended sediment particle in turbulent flows is modeled as a stochastic diffusion process, which is composed of a drift term and a random term. The stochastic formula of fluid velocity is then substituted into the advection-diffusion (AD) equation to obtain the stochastic partial differential equation (SPDE) for suspended sediment transport. The lattice approximation is applied to solve the SPDE of suspended sediment transport in open channel flow. The proposed model, explicitly expressing the randomness of sediment concentration, has the advantage of capturing any randomly selected scenarios of particle movement and thus a more comprehensive quantitative description of sediment concentrations compared with the deterministic AD equation. As a result, the probability distribution of the sediment transport rate can be characterized based on a number of realizations obtained in the numerical experiments. It is found from the numerical experiments of particle trajectory that the transport of sediment particles is in the form of fully suspended load when the Rouse number is less than one. The ensemble mean sediment concentration of the proposed SPDE, obtained by the Monte Carlo simulation, agrees well with that of the deterministic AD equation.