Numerical Studies of Three-dimensional Stochastic Darcy’s Equation and Stochastic Advection-Diffusion-Dispersion Equation

Abstract  Solute transport in randomly heterogeneous porous media is commonly described by stochastic flow and advection-dispersion
equations with a random hydraulic conductivity field. The statistical distribution of conductivity of engineered and naturally
occurring porous material can vary, depending on its origin. We describe solutions of a three-dimensional stochastic advection-dispersion
equation using a probabilistic collocation method (PCM) on sparse grids for several distributions of hydraulic conductivity.
Three random distributions of log hydraulic conductivity are considered: uniform, Gaussian, and truncated Gaussian (beta).
Log hydraulic conductivity is represented by a Karhunen-Loève (K-L) decomposition as a second-order random process with an
exponential covariance function. The convergence of PCM has been demonstrated. It appears that the accuracy in both the mean
and the standard deviation of PCM solutions can be improved by using the Jacobi-chaos representing the truncated Gaussian
distribution rather than the Hermite-chaos for the Gaussian distribution. The effect of type of distribution and parameters
such as the variance and correlation length of log hydraulic conductivity and dispersion coefficient on leading moments of
the advection velocity and solute concentration was investigated.

• Content Type Journal Article
• DOI 10.1007/s10915-010-9346-5
• Authors
  
  
  • G. Lin, Pacific Northwest National Laboratory Computational Mathematics 902 Battelle Blvd. Box 999 Richland WA 99352 USA
  • A. M. Tartakovsky, Pacific Northwest National Laboratory Computational Mathematics 902 Battelle Blvd. Box 999 Richland WA 99352 USA
  
  

• Journal Journal of Scientific Computing
• Online ISSN 1573-7691
• Print ISSN 0885-7474

Published by

Original source : http://www.springerlink.com/content/0098461gn72102...