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The Mathematics of Fluid Flow Through Porous Media - by Myron B Allen (Hardcover)
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Highlights
- Master the techniques necessary to build and use computational models of porous media fluid flow In The Mathematics of Fluid Flow Through Porous Media, distinguished professor and mathematician Dr. Myron B. Allen delivers a one-stop and mathematically rigorous source of the foundational principles of porous medium flow modeling.
- About the Author: Myron B. Allen, is Professor Emeritus of Mathematics at the University of Wyoming in Laramie, Wyoming, USA.
- 224 Pages
- Mathematics, Applied
Description
About the Book
"The book will fill a gap that has emerged as computational modeling has become a standard tool in porous media research. As the field has advanced, early-career researchers such as graduate students understandably gloss over some mathematical fundamentals to begin working on computational problems at the frontiers. The proposed book will furnish a pathway by which these researchers can efficiently acquire the fundamentals needed to become well-informed users and designers of computational models. The book will introduce several advanced techniques, such as the method of characteristics, fundamental solutions, similarity methods, and dimensional analysis in a self-contained fashion that will be accessible to students who have not previously encountered these concepts. The author has taught a course based on this material four times to audiences that included graduate students from Mathematics, Civil Engineering, Petroleum Engineering, Soil Science, and Geophysics. The course has received highly favorable student reviews"--Book Synopsis
Master the techniques necessary to build and use computational models of porous media fluid flow
In The Mathematics of Fluid Flow Through Porous Media, distinguished professor and mathematician Dr. Myron B. Allen delivers a one-stop and mathematically rigorous source of the foundational principles of porous medium flow modeling. The book shows readers how to design intelligent computation models for groundwater flow, contaminant transport, and petroleum reservoir simulation.
Discussions of the mathematical fundamentals allow readers to prepare to work on computational problems at the frontiers of the field. Introducing several advanced techniques, including the method of characteristics, fundamental solutions, similarity methods, and dimensional analysis, The Mathematics of Fluid Flow Through Porous Media is an indispensable resource for students who have not previously encountered these concepts and need to master them to conduct computer simulations.
Teaching mastery of a subject that has increasingly become a standard tool for engineers and applied mathematicians, and containing 75 exercises suitable for self-study or as part of a formal course, the book also includes:
- A thorough introduction to the mechanics of fluid flow in porous media, including the kinematics of simple continua, single-continuum balance laws, and constitutive relationships
- An exploration of single-fluid flows in porous media, including Darcy's Law, non-Darcy flows, the single-phase flow equation, areal flows, and flows with wells
- Practical discussions of solute transport, including the transport equation, hydrodynamic dispersion, one-dimensional transport, and transport with adsorption
- A treatment of multiphase flows, including capillarity at the micro- and macroscale
Perfect for graduate students in mathematics, civil engineering, petroleum engineering, soil science, and geophysics, The Mathematics of Fluid Flow Through Porous Media also belongs on the bookshelves of any researcher who wishes to extend their research into areas involving flows in porous media.
From the Back Cover
Master the concepts needed to build and use mathematical models of porous media flow
In The Mathematics of Fluid Flow Through Porous Media, distinguished professor and mathematician Dr. Myron B. Allen delivers a one-stop, mathematically rigorous introduction to the foundations of porous medium flow modeling, including groundwater flow, contaminant transport, and petroleum reservoir flows.
Insights into mathematical fundamentals prepare readers to work on computational problems at the frontiers of the field. Introducing several analytical techniques, including the method of characteristics, fundamental solutions, similarity methods, and dimensional analysis, The Mathematics of Fluid Flow Through Porous Media provides an indispensable resource for students who have not previously encountered these concept. Covering a subject that has grown steadily in importance and mathematical depth for over 150 years, and containing 75 exercises suitable for self-study or as part of a formal course, this book also includes:
- A practical introduction to the mechanics of fluid flow in porous media, including kinematics single- and multi-continuum balance laws, and constitutive relationships
- An exploration of single-fluid flows including Darcy's Law, non-Darcy flows, the single-fluid flow equation, areal flows, flows with wells, and permeability tensors
- An analysis of solute transport, including the transport equation, hydrodynamic dispersion, the advection-diffusion equation and transport with adsorption
- A treatment of multiphase flows, including capillarity and the partial differential equations governing variably saturated, two-fluid, three-fluid, and compositional flows
Perfect for graduate students in mathematics, civil engineering, petroleum engineering, soil science, and geophysics, The Mathematics of Fluid Flow Through Porous Media also belongs on the bookshelves of any researcher who wishes to extend their research into areas involving flows in porous media.
About the Author
Myron B. Allen, is Professor Emeritus of Mathematics at the University of Wyoming in Laramie, Wyoming, USA. He is the author of Continuum Mechanics: The Birthplace of Mathematical Models and co-author of the first and second editions of Numerical Analysis for Applied Science.