The past 4 decades have witnessed an increasing concern worldwide for
environmental quality and management. This concern has been for land,
water, and air resources as well as ecosystems. Concern for water
resources has extended to water over and below the land surface (i.e.,
surface water, unsaturated water, and groundwater), atmospheric water,
oceanic waters, as well as snow, ice, and glacier resources.
Fundamental to sustained environmental quality and management is
solute transport. As a result, a huge amount of literature, including
journal papers, technical reports, conference proceedings papers, and
books has been published and continues to be published. This is
particularly true in the area of groundwater. This book deals with
solute transport modeling in groundwater.
This is a small book comprising 7 chapters encompassing 205 pages.
Chapter 1 introduces main physical and chemical transport processes,
derives the transport equation, and discusses the mathematical
nature of the equation along with initial and boundary conditions. The
discussion in the chapter is presented clearly and is quite easy to
understand, even if one has no prior background in the area.
Illustrations supplementing the discussion make the reading enjoyable.
Chapter 2 presents analytical solutions of the transport equation
under different conditions. For one dimensional transport, solutions
are provided for instantaneous source, continuous source, and
finite-duration source. Two dimensional transport solutions include
instantaneous source, continuous source, steady-state plume, and
finite aquifer. Analytical solutions are supplemented with a concise
and meaningful discussion.
Recognizing the limitations of analytical solutions, grid-based
numerical methods are presented in Chapter 3. These methods include
finite-difference method, finite-volume method, and finite-element
method. The chapter discusses numerical schemes for time
discretization of the transport equation first, such as explicit
Euler method, implicit Euler method, Crank-Nicholson method, and
higher order methods, the chapter then goes on to discuss mass balance
for ID as well as 2D finite difference. Criteria for numerical
stability as well as precision are included in the discussion.
Finite-volume method is discussed next. Triangulation and dual grids,
approximation functions and mass balance, upwind stabilisation, and
incorporation of boundary conditions are included in the discussion.
The discussion of the finite- element method includes Galerkin method,
stabilisation, boundary conditions, and adaptive "ridding. The chapter
is quite easy to follow and is clear and to-the-point in presentation.
Numerical methods based on particle tracking constitutes the subject
matter of Chapter 4. Discussed in this method are the Bowline and
travel-time method, characteristics method, and random-walk method.
The chapter is concluded with a discussion on the comparison of these
methods as well as the numerical methods presented in the previous
Chapter 5 discusses methods for obtaining solutions of systems of
equations that appear in the methods presented in Chapters 3 and 4.
These methods include direct solution, classical linear iterative
methods, conjugate-gradient method, multigrid methods, and the
Newton-Raphson method. The discussion of the methods is clear and
Transport and reactions are presented in Chapter 6. Retardation, dual
porosity model, multispecies models, coupling of transport and
reactions, and an example application of multispecies simulation are
included in the chapter. The discussion in the chapter is
Chapter 7 deals with transport in fractured media, including flow and
transport in a single fracture, equivalent porous media approach,
multidomain approach, discrete fracture approach, and modeling
strategies. The chapter provides a good and comprehensive discussion.
On the whole the book is well written, is easy to follow, and concise.
A significant amount of the literature cited in the text is older than
10 years. It would have been desirable if it had presented the
inherent difficulties in dealing with solute transport in groundwater,
especially from the point of view of uncertainties associated with
mathematical formulations being employed these days and the resulting
errors and the reliability of different formulations for different
conditions. The book will serve as a good text for a course on solute
transport either at the senior undergraduate level or the beginning
graduate level. It would also be useful to have this book on one's
Vijay P. Singh
Journal of Hydrologic Engineering, Sept/Oct 2006, p. 512