Uncertainty quantification using multiscale methods for porous media flows

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Title: Uncertainty quantification using multiscale methods for porous media flows
Author: Dostert, Paul Francis
Abstract: 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 .
URI: http : / /hdl .handle .net /1969 .1 /ETD -TAMU -2532
Date: 2009-05-15

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Uncertainty quantification using multiscale methods for porous media flows. Available electronically from http : / /hdl .handle .net /1969 .1 /ETD -TAMU -2532 .

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