HR: 1340h
AN: H23B-1318 [Abstracts]
TI: An efficient, high-order multi-element probabilistic collocation method on sparse grids for three-dimensional flow in random porous media
AU: * Lin, G
EM: guang.lin@pnl.gov
AF: Pacific Northwest National Laboratory, P.O. BOX 999, MS K6-08, Richland, WA 99352,
United States
AU: Tartakovsky, A M
EM: alexandre.tartakovsky@pnl.gov
AF: Pacific Northwest National Laboratory, P.O. BOX 999, MS K6-08, Richland, WA 99352,
United States
AB:
In this study, we use a multi-element probabilistic collocation method (ME-
PCM) on sparse grids to obtain high-order solutions of the mean and standard
deviation of hydraulic head and concentration for three-dimensional saturated
flow and transport in randomly heterogeneous porous media.
First, Karhunen-Loeve (K-L) decomposition is applied to represent the log hydraulic conductivity Y = lnK. The
hydraulic head h and Darcy flux q are obtained by solving the three-dimensional continuity equation coupled
with Darcy's law with random hydraulic conductivity field. The concentration is computed by solving the three-
dimensional stochastic
advection-dispersion-reaction equation with random Darcy flux q.
ME-PCM is an extension of multi-element generalized polynomial chaos
(ME-gPC). ME-PCM couples ME-gPC with probabilistic collocation. By using
the sparse grid points, ME-PCM can handle random process with large number
of random dimensions with relatively lower computational cost, compared to
full tensor products.
Monte Carlo (MC) simulations were conducted to verify the ME-PCM solution. By comparing the MC and ME-PCM
results, it is evident that the ME-PCM approach is computationally more efficient than Monte Carlo simulations.
Unlike the conventional moment-equation approach, there is no limitation on the amplitude of random
perturbations for ME-PCM. Furthermore, ME-PCM
on sparse grids can efficiently simulate flow and transport in randomly heterogeneous porous media with small
correlation lengths. The effect of correlation lengths and variance of hydraulic conductivity on flow and transport
has also been investigated.
DE: 1846 Model calibration (3333)
DE: 1847 Modeling
DE: 1873 Uncertainty assessment (3275)
SC: Hydrology [H]
MN: 2007 Fall Meeting