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Reading Room :: Theses 2000
Qin Lu's dissertation
by
Qin Lu, Ph.D.
University of Texas at Austin, 2000
Supervisor: Mary Fanett Wheeler
he main purpose of this dissertation is to investigate
accurate and efficient numerical techniques for simulation of
multi-phase / multi-component flow and transport phenomena in porous
media which are of major importance in the petroleum and environmental
industries. We propose to emphasize a novel numerical methodology,
which is called the multi-block algorithm. This algorithm is based on
the decomposition of the simulation domain into multiple
non-overlapping subdomains (blocks) according to the geological,
geometric and physical / chemical properties. One then applies the
most suitable grid, numerical scheme and physical model in each
subdomain, so that the computational cost is reduced and accuracy is
preserved. Across the interface of neighboring subdomains, the
consistent primary variables and the continuity of the component
mass fluxes are imposed in a weak sense.
In this dissertation we first discuss the mathematical and numerical
formulations of physical models, such as the implicit black-oil model,
the implicit and IMPES two-phase hydrology models. We then formulate
the multi-block black-oil model coupling different grids, which can be
non-matching on the interface. In addition, we define the multi-model
couplings; in particular, the coupling of the implicit and IMPES
schemes for two-phase immiscible flow, and the coupling of the
implicit three-phase black-oil model and the implicit two-phase
hydrology model. Computational examples are presented to demonstrate
the scalability of the multi-block / multi-model simulators over the
traditional single-block / single-model simulators. Excellent
agreements of the results between these two approaches are shown.
Parallel computation issues, especially the MPI (Message Passing
Interface) multi-communicator implementation and model-based load
balancing strategies for the parallelism of the multi-model problem
are also considered. Summary of these results is presented in the last
chapter.
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