An efficient, high-order probabilistic collocation method on sparse grids for three-dimensional flow and solute transport in randomly heterogeneous porous media

Research output: Contribution to journalArticle

Abstract

In this study, a probabilistic collocation method (PCM) on sparse grids is used to solve stochastic equations describing flow and transport in three-dimensional, saturated, randomly heterogeneous porous media. The Karhunen-Loève decomposition is used to represent log hydraulic conductivity Y = ln Ks. The hydraulic head h and average pore-velocity v are obtained by solving the continuity equation coupled with Darcy's law with random hydraulic conductivity field. The concentration is computed by solving a stochastic advection-dispersion equation with stochastic average pore-velocity v computed from Darcy's law. The PCM approach is an extension of the generalized polynomial chaos (gPC) that couples gPC with probabilistic collocation. By using sparse grid points in sample space rather than standard grids based on full tensor products, the PCM approach becomes much more efficient when applied to random processes with a large number of random dimensions. Monte Carlo (MC) simulations have also been conducted to verify accuracy of the PCM approach and to demonstrate that the PCM approach is computationally more efficient than MC simulations. The numerical examples demonstrate that the PCM approach on sparse grids can efficiently simulate solute transport in randomly heterogeneous porous media with large variances.

Original languageEnglish (US)
Pages (from-to)712-722
Number of pages11
JournalAdvances in Water Resources
Volume32
Issue number5
DOIs
StatePublished - May 2009
Externally publishedYes

Keywords

  • Heterogeneous porous media
  • Probabilistic collocation
  • Solute transport
  • Stochastic method

ASJC Scopus subject areas

  • Water Science and Technology

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