The authors, all of them groundwater modelling professionals, focus on the detailed presentation of numerical methods commonly used in transport models, to provide practitioners with a sound theoretical basis for transport model applications. Grid-based methods are presented, including explicit and implicit finite differences, finite elements and finite volume methods. Particle tracking techniques are also covered, among them the method of characteristics and the random-walk method.

This professional text addresses academics, scientists, engineers, hydrologists and hydrogeol ogists interested in the application of transport models in hydrogeology, geoecology, hydrology, geography, environmental engineering, hydraulic engineering and water economics.

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.

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 concise.

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 comprehensive.

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 bookshelf.

Vijay P. Singh

Journal of Hydrologic Engineering, Sept/Oct 2006, p. 512