Path integral approach to Darcy flow

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Title: Path integral approach to Darcy flow
Authors: Westbroek, Marise
Item Type: Thesis or dissertation
Abstract: We explore a path integral approach to Darcy flow through a stochastic permeable medium. In one dimension, Darcy's law can be solved exactly. We give a derivation of the path integral used to obtain the Darcy pressure statistics. We also outline the computational setup for the conventional finite-volume method and the implementation of a stochastic field generator. We provide a detailed user's guide to the calculation of path integrals on a lattice, including an explicit computational setup and corresponding pseudocode. The higher-dimensional form of Darcy's law lacks an analytic solution. We show that the simulated annealing algorithm provides a viable alternative to simulating a path integral for Darcy's law. We compare the results for the path integral and simulated annealing methods to those for the finite-volume method. All comparisons pass a Kolmogorov-Smirnov test at the 95% confidence level. We discuss log-normal and Gaussian fits to the pressure statistics. Finally, we make a number of suggestions for future work, such as the use of the renormalization group and the extension of Darcy's law to multiphase flow.
Content Version: Open Access
Issue Date: Jan-2019
Date Awarded: Mar-2019
Copyright Statement: Creative Commons Attribution NonCommercial NoDerivatives Licence
Supervisor: King, Peter R.
Vvedensky, Dimitri D.
Sponsor/Funder: Imperial College London
Engineering and Physical Sciences Research Council
Funder's Grant Number: EP/L015579/1
Department: Earth Science & Engineering
Publisher: Imperial College London
Qualification Level: Doctoral
Qualification Name: Doctor of Philosophy (PhD)
Appears in Collections:Earth Science and Engineering PhD theses

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