Stochastic finite element model for transient advective-dispersive transport in an uncertain hydrodynamic environment
A finite element formulation that incorporates a first-order second-moment (FOSM) algorithm is developed for the uncertainty analysis of groundwater solute transport in saturated, isotropic media. The contaminant concentration is the state random variable resulting from two major uncertain hydrodynamic parameters: hydraulic conductivity and dispersivity. Applying a Taylor's series expansion, the mean and standard deviation of solute concentration are calculated directly. This algorithm has the flexibility of accommodating steady or unsteady solute transport with any type of uncertain hydraulic parameter. A set of two-dimensional examples with one and two uncertain parameters in homogeneous and heterogeneous media is presented to demonstrate the applicability of proposed method. These examples are compared to the exact solution from a convolution integral approach and show that the proposed FOSM method is far more cost-effective than Monte Carlo simulation. The numerical error resulting from the FOSM method and potential methods for reducing the error are also discussed in this paper.
