Reduced order model and uncertainty quantification for stochastic porous media flows.

Bibliographic Details
Main Author: Wei, Jia
Other Authors: Efendiev, Yalchin (Thesis advisor), Datta-Gupta, Akhil (Thesis advisor)
Format: Thesis eBook
Language:English
Published: [College Station, Tex.] : [Texas A&M University], [2012]
Subjects:
Online Access:Link to OAK Trust copy

MARC

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100 1 |a Wei, Jia. 
245 1 0 |a Reduced order model and uncertainty quantification for stochastic porous media flows. 
264 1 |a [College Station, Tex.] :  |b [Texas A&M University],  |c [2012] 
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502 |b Doctor of Philosophy  |c Texas A&M University  |d 2012  |o http://hdl.handle.net/1969.1/ETD-TAMU-2012-08-11598 
504 |a Includes bibliographical references. 
516 |a Text (Dissertation) 
520 3 |a In this dissertation, we focus on the uncertainty quantification problems where the goal is to sample the porous media properties given integrated responses. We first introduce a reduced order model using the level set method to characterize the channelized features of permeability fields. The sampling process is completed under Bayesian framework. We hence study the regularity of posterior distributions with respect to the prior measures. The stochastic flow equations that contain both spatial and random components must be resolved in order to sample the porous media properties. Some type of upscaling or multiscale technique is needed when solving the flow and transport through heterogeneous porous media. We propose ensemble-level multiscale finite element method and ensemble-level preconditioner technique for solving the stochastic flow equations, when the permeability fields have certain topology features. These methods can be used to accelerate the forward computations in the sampling processes. Additionally, we develop analysis-of-variance-based mixed multiscale finite element method as well as a novel adaptive version. These methods are used to study the forward uncertainty propagation of input random fields. The computational cost is saved since the high dimensional problem is decomposed into lower dimensional problems. We also work on developing efficient advanced Markov Chain Monte Carlo methods. Algorithms are proposed based on the multi-stage Markov Chain Monte Carlo and Stochastic Approximation Monte Carlo methods. The new methods have the ability to search the whole sample space for optimizations. Analysis and detailed numerical results are presented for applications of all the above methods. 
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653 |a ensemble-level 
653 |a analysis of variance 
653 |a preconditioner 
653 |a regularity of posterior 
700 1 |a Efendiev, Yalchin,  |e thesis advisor. 
700 1 |a Datta-Gupta, Akhil,  |e thesis advisor. 
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