In this dissertation we discuss numerical methods used for uncertainty quantifi-
cation applications to flow in porous media. We consider stochastic flow equations
that contain both a spatial and random component which must be resolved in our numerical
models. When solving the flow and transport through heterogeneous porous
media some type of upscaling or coarsening is needed due to scale disparity. We describe
multiscale techniques used for solving the spatial component of the stochastic
flow equations. These techniques allow us to simulate the flow and transport processes
on the coarse grid and thus reduce the computational cost. Additionally, we
discuss techniques to combine multiscale methods with stochastic solution techniques,
specifically, polynomial chaos methods and sparse grid collocation methods.
We apply the proposed methods to uncertainty quantification problems where the
goal is to sample porous media properties given an integrated response. We propose
several efficient sampling algorithms based on Langevin diffusion and the Markov
chain Monte Carlo method. Analysis and detailed numerical results are presented
for applications in multiscale immiscible flow and water infiltration into a porous
medium.
| Identifer | oai:union.ndltd.org:tamu.edu/oai:repository.tamu.edu:1969.1/ETD-TAMU-2532 |
| Date | 15 May 2009 |
| Creators | Dostert, Paul Francis |
| Contributors | Efendiev, Yalchin |
| Source Sets | Texas A and M University |
| Language | en_US |
| Detected Language | English |
| Type | Book, Thesis, Electronic Dissertation, text |
| Format | electronic, application/pdf, born digital |
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