| Chemical Engineering Graduate Seminars |
Friday, February 23, 2007
Stochastic Uncertainty Quantification Approaches for Large Scale Subsurface Problems
Professor Dongxiao Zhang
Petroleum and Geological Engineering The University of Oklahoma
Abstract
Prediction of subsurface flow and transport is subject to uncertainties, which can result from the heterogeneity of the media and our incomplete knowledge about their properties. Such uncertainties render the model parameters random and the equations describing flow and transport in the media stochastic. Monte Carlo simulation method (MCS) is the most common and conceptually straightforward approach. However, it requires large computational efforts, especially for large scale problems. Recently, a number of alternative stochastic approaches have been developed to quantifying prediction uncertainties. This talk discusses four representative methods: The moment equation method (ME); the Galerkin polynomial chaos expansion method (PCE); the Karhunen-Loeve based moment equation method (KLME); and the probabilistic collocation method (PCM). The efficiency of these methods depends on how the random (probability) space is approximated. Detailed theoretical analyses and numerical computations are performed to compare these methods against MCS in terms of accuracy, efficiency, validity range, and compatibility with existing deterministic simulators. It is found that the KLME, PCE and PCM are generally more efficient than the MCS and the ME for larger-scale problems. The expansions in representing the dependent random fields and the ways for evaluating the expansion coefficients distinguish among the KLME, PCE and PCM.
URL:
http://www-rcf.usc.edu/~donzhang/
Friday, February 23, 2007 Seminar at 11:15 a.m. HED 116
The Scientific Community is cordially invited
