viii
Preface
modeling that have not yet been adequately solved. The first one is called the
"scale effect problem." The identified dispersivities may vary with the scale of
experiment and the size of element of numerical discretization. The second
one is called the "numerical dispersion problem." Sharp concentration fronts
are difficult to simulate accurately using a numerical method. The third
difficulty is caused by the "uncertainty enlargement problem." The uncertainties associated with hydraulic conductivities, porosities and head distributions may be enlarged and propagated to the calculation of velocity fields
through Darcy's Law. Incorrect velocity distributions may cause large computational error in the determination of both advection and dispersion components of contaminant transport and fate. The fourth difficulty is caused
by the "data insufficient problem." Tracer tests can only be carried out
on a small region and it is difficult to observe concentration plumes in threedimensional space. Generally, we do not have enough data for calibrating
the mass transport model of regional problems. These difficulties make the
modeling of groundwater quality more challenging than the modeling of
groundwater flow. Although the importance of mathematical modeling in the
study of groundwater quality problems is significant, the accuracy of a mass
transport model and, thus, the reliability of management decisions derived
from the model, are often questionable.
This book introduces all primary aspects of groundwater quality modeling. The emphasis, however, is on numerical techniques. Besides introducing
basic concepts, theories, methods and applications, special attentions are
paid to three-dimensional models, model selection criteria, tracer test design,
dispersion parameter identification, and reliability analysis. The overall
purpose is to develop an applicable methodology for groundwater quality
modeling. This book is designed to provide a course text at the graduate
level. The materials are presented in such a manner that the book can also
be used as a reference for hydrogeologists, geochemists and environmental
engineers.
Chapter 1 is an introduction, in which the problem ofmodeling groundwater pollution is depicted, and the relationships between simulation, parameter identification, and groundwater quality management are explained.
Advection-Dispersion equations (ADE) that can simulate multi-component transport in multi-phase flow are derived in Chapter 2. Hydrodynamic
dispersion coefficients and other parameters in the ADE are defined. Various
combinations of sink/source terms, initial conditions, and boundary conditions are listed.
Chapter 3 gives analytical solutions for some one-, two-, and threedimensional advection-dispersion problems. Several often-used techniques
for finding analytical solutions are introduced.
In Chapter 4, conditions of convergency and stability of finite difference
methods for solving the ADE are presented. The phenomena of overshoot
and numerical dispersion associated with finite difference solutions for prob-
Preface
modeling that have not yet been adequately solved. The first one is called the
"scale effect problem." The identified dispersivities may vary with the scale of
experiment and the size of element of numerical discretization. The second
one is called the "numerical dispersion problem." Sharp concentration fronts
are difficult to simulate accurately using a numerical method. The third
difficulty is caused by the "uncertainty enlargement problem." The uncertainties associated with hydraulic conductivities, porosities and head distributions may be enlarged and propagated to the calculation of velocity fields
through Darcy's Law. Incorrect velocity distributions may cause large computational error in the determination of both advection and dispersion components of contaminant transport and fate. The fourth difficulty is caused
by the "data insufficient problem." Tracer tests can only be carried out
on a small region and it is difficult to observe concentration plumes in threedimensional space. Generally, we do not have enough data for calibrating
the mass transport model of regional problems. These difficulties make the
modeling of groundwater quality more challenging than the modeling of
groundwater flow. Although the importance of mathematical modeling in the
study of groundwater quality problems is significant, the accuracy of a mass
transport model and, thus, the reliability of management decisions derived
from the model, are often questionable.
This book introduces all primary aspects of groundwater quality modeling. The emphasis, however, is on numerical techniques. Besides introducing
basic concepts, theories, methods and applications, special attentions are
paid to three-dimensional models, model selection criteria, tracer test design,
dispersion parameter identification, and reliability analysis. The overall
purpose is to develop an applicable methodology for groundwater quality
modeling. This book is designed to provide a course text at the graduate
level. The materials are presented in such a manner that the book can also
be used as a reference for hydrogeologists, geochemists and environmental
engineers.
Chapter 1 is an introduction, in which the problem ofmodeling groundwater pollution is depicted, and the relationships between simulation, parameter identification, and groundwater quality management are explained.
Advection-Dispersion equations (ADE) that can simulate multi-component transport in multi-phase flow are derived in Chapter 2. Hydrodynamic
dispersion coefficients and other parameters in the ADE are defined. Various
combinations of sink/source terms, initial conditions, and boundary conditions are listed.
Chapter 3 gives analytical solutions for some one-, two-, and threedimensional advection-dispersion problems. Several often-used techniques
for finding analytical solutions are introduced.
In Chapter 4, conditions of convergency and stability of finite difference
methods for solving the ADE are presented. The phenomena of overshoot
and numerical dispersion associated with finite difference solutions for prob-