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Preface
Seldom turns out the way it does in the song.
Robert Hunter
This book provides a semester‐length course in the mathematics of fluid flows in porous media. Over a 20‐year span, I taught such a course every few years to doctoral students in engineering, mathematics, and geophysics. Most of these students' research involved flow and transport in groundwater aquifers, soils, and petroleum reservoirs. The students' mathematical backgrounds ranged from standard undergraduate engineering requirements to more advanced, graduate‐level training.
The book emphasizes analytic aspects of flows in porous media. This focus may seem odd: Most mathematically oriented scholarship in the area is computational in nature, owing both to the heterogeneity of natural porous media and to the inherent nonlinearity of many underground flow models. Nevertheless, while many superb books cover computational methods for flows in porous media, intelligent design of numerical approximations also requires a grasp of certain analytic questions:
Where do the governing equations come from?
What physics do they model, and what physics do they neglect?
What qualitative properties do their solutions exhibit?
Where appropriate, the book discusses numerical implications of these questions.