In this dissertation we develop, analyze and implement effective numerical methods
for multiscale phenomena arising from flows in heterogeneous porous media. The
main purpose is to develop innovative numerical and analytical methods that can
capture the effect of small scales on the large scales without resolving the small scale
details on a coarse computational grid. This research activity is strongly motivated
by many important practical applications arising in contaminant transport in heterogeneous
porous media, oil reservoir simulations and subsurface characterization.
In the work, we investigate three main multiscale numerical methods, i.e., multiscale
finite element method, partition of unity method and mixed multiscale finite
element method. These methods employ limited single or multiple global information.
We apply these numerical methods to partial differential equations (elliptic,
parabolic and wave equations) with continuum scales. To compute the solution of
partial differential equations on a coarse grid, we define global fields such that the solution
smoothly depends on these fields. The global fields typically contain non-local
information required for achieving a convergence independent of small scales. We
present a rigorous analysis and show that the proposed global multiscale numerical
methods converge independent of small scales. In particular, a global mixed multiscale
finite element method is extensively studied and applied to two-phase flows. We present some numerical results for two-phase simulations on coarse grids. The
numerical results demonstrate that the global multiscale numerical methods achieve
high accuracy.
| Identifer | oai:union.ndltd.org:tamu.edu/oai:repository.tamu.edu:1969.1/ETD-TAMU-2991 |
| Date | 15 May 2009 |
| Creators | Jiang, Lijian |
| 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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