PNNL

Abstract

In this study, we solve the three-dimensional stochastic Darcy's equation and stochastic advection-diffusion-dispersion equation using a probabilistic collocation method (PCM) on sparse grids. Karhunen-Lo\`{e}ve (KL) decomposition is employed to represent the three-dimensional log hydraulic conductivity $Y=\ln K_s$. The numerical examples which demonstrate the convergence of PCM are presented. It appears that the faster convergence rate in the variance can be obtained by using the Jacobi-chaos representing the truncated Gaussian distributions than using the Hermite-chaos for the Gaussian distribution. The effect of dispersion coefficient on the mean and standard deviation of the hydraulic head and solute concentration is investigated. Additionally, we also study how the statistical properties of the hydraulic head and solute concentration vary while using different types of random distributions and different standard deviations of random hydraulic conductivity.