This dissertation considers the effect of measuring randomly varying local hydraulic conductivity K(x) on one's ability to predict transient flow within bounded domains, driven by random sources, initial head distribution, and boundary functions. The first part of this work extends the steady state nonlocal formalism by Neuman and Orr [1992] in order to obtain the prediction of local hydraulic head h(x, t) and Darcy flux q(x, t) by means of their ensemble moments <h(x, t)> (c) and <q(x, t)>(c)conditioned on measurements of K(x). These predictors satisfy a deterministic flow equation which contains a nonlocal in space and time term called a "residual flux". As a result, <q(x, t)>(c) is nonlocal and non-Darcian so that an effective hydraulic conductivity K(c) does not generally exist. It is shown analytically that, with the exception of several specific cases, the well known requirement of "slow time-space variation" in uniform mean hydraulic gradient is essential for the existence of K(c). In a subsequent chapter, under this assumption, we develop analytical expressions for the effective hydraulic conductivity for flow in a three dimensional, mildly heterogeneous, statistically anisotropic porous medium of both infinite extent and in the presence of randomly prescribed Dirichlet and Neumann boundaries. Of a particular interest is the transient behavior of K(c) and its sensitivity to degree of statistical anisotropy and domain size. In a bounded domain, K(c) (t) decreases rapidly from the arithmetic mean K(A) at t = 0 toward the effective hydraulic conductivity corresponding to steady state flow, K(sr), K(c), exhibits similar behavior as a function of the dimensionless separation distance ρ between boundaries. At ρ = 0, K(c) = K(A) and rapidly decreases towards an asymptotic value obtained earlier for an infinite domain by G. Dagan. Our transient nonlocal formalism in the Laplace space allows us to analyze the impact of other than slow time-variations on the prediction of <q(x, t)>(c),. Analyzing several functional dependencies of mean hydraulic gradient, we find that this assumption is heavily dependent on the (relaxation) time-scale of the particular problem. Finally, we formally extend our results to strongly heterogeneous porous media by invoking the Landau-Lifshitz conjecture.

No description available.

No description available.

No description available.

The issue of local scale and smoothness presents a crucial and daunting challenge for numerical simulation methods in fluid dynamics. Yet in the interests of both accuracy and economy, how can one devise a general technique that efficiently resolves flow features of consequence and discriminates against others which are either ``negligible' or amenable to ``universal' modeling? This is particularly difficult because geometries of engineering interest are complex and multi-dimensional, precluding a priori knowledge of the flowfield. To address this challenge, the current work employs wavelet theory for the local scale decomposition of functions, which provides a natural mechanism for the adaptive compression of data. The resulting technique is known as the Multi-Resolution Discontinuous Galerkin (MRDG) method. This research successfully demonstrates that the multi-resolution framework and the discontinuous Galerkin method are well-suited for a new approach to accuracy and cost as demonstrated by the relative ease of their integration in spatial dimension greater than one. Some specific steps achieved include the implementation of suitable data encoding and compression algorithms, construction of multi-wavelet expansion bases in one and two dimensions, and derivation of the multi-resolution derivative operator that includes an upwind-type correction to the central scheme. Solutions with the MRDG method are observed to adapt to and track both smooth and discontinuous flow features in an entirely solution-driven manner without the need for a priori user knowledge of those flow features. Run-time efficiency and local adaptation characteristics are explored via a series of classic test problems.

Thesis (M. Eng.(Mechanical and Aeronautical Engineering))--Universiteit van Pretoria, 2007. / Abstract in English. Includes bibliographical references.

Thesis (M.S.)--Rochester Institute of Technology, 1996. / Typescript. Includes bibliographical references (leaves [159]-[161]).

Thesis (Ph. D.)--Rutgers University, 2008. / "Graduate Program in Mechanical and Aerospace Engineering." Includes bibliographical references (p. 152-163).

Thesis (Ph. D.)--Oregon State University, 2010. / Printout. Includes bibliographical references (leaves 109-115). Also available on the World Wide Web.

Thesis (Ph. D.)--Ohio State University, 2006. / Title from first page of PDF file. Includes bibliographical references (p. 211-230).