7.1. The Classification of Groundwater Quality Models
193
Besides the above cases, some other hydrodynamic dispersion models,
such as the water quality in three-dimensional unsaturated zones, the water
quality in multilayer leaking aquifers, and so on, can also be listed without
difficulty.
From the charts shown in Figures 7.1 and 7.2, we can see that the solution
of hydrodynamic dispersion models consists of two parts-solving the flow
equation and the advection-dispersion equation separately or simultaneously. We have introduced various numerical methods for handling these
two kinds of equations. As a result, now we are able to use these numerical
methods to solve the advection-dispersion models in various cases.
7.1.3 Pure Advection Models
Hydrodynamic dispersion always creates a transition zone between tracer
marked water and unmarked water. However, if the width of the transition
zone is relatively small in comparison with the study area, the pure advection
model may be adopted without considering the effect of dispersion. This case
may be encountered when the contamination is caused by agriculture, seawater intrusion, artificial rech arge, and so on. As a result, the difficulty in
determining the dispersion coefficient is avoided.
There are two kinds of pure advection models. The first one uses a flow
equation only, and the second one requires coupling of a flow equation with
a quality equation, but without considering the dispersion. They are described below.
1. Solute Transport Prediction with Flow Equation Only
With the transition zone neglected, it is assumed that there is an abrupt
interface between two different bodies of water with different qualities. The
abrupt interface is also called a front, which moves uninterruptedly with the
development of pollution or the transportation of the solute. The problem is
how to determine the location of this moving front. Let us introduce a
numerical method, which is very simple in concept, for solving this problem.
Suppose the location of the front at time t is known and is described by a
set of points on the front. The velocities of these points at moment t can be
calculated by the solution of the flow equation and Darcy's law. Assume that
point i is located at [Xi(t), Yi(t), Zi(t)] at time t, and the components ofvelocity
are l'i,At), l'i,y(t), l'i,Z
{
Xi(t + Ilt) ~ Xi(t) + l'i,At) 'Ilt,
Yi(t + ilt) ~ Yi(t) + l'i,y(t) 'Ilt,
Zi(t + ilt) ~ Zi(t) + l'i,z(t) ·Ilt.
(7.1.15)
When all the locations of these points at t + Ilt are obtained, the approxi-
193
Besides the above cases, some other hydrodynamic dispersion models,
such as the water quality in three-dimensional unsaturated zones, the water
quality in multilayer leaking aquifers, and so on, can also be listed without
difficulty.
From the charts shown in Figures 7.1 and 7.2, we can see that the solution
of hydrodynamic dispersion models consists of two parts-solving the flow
equation and the advection-dispersion equation separately or simultaneously. We have introduced various numerical methods for handling these
two kinds of equations. As a result, now we are able to use these numerical
methods to solve the advection-dispersion models in various cases.
7.1.3 Pure Advection Models
Hydrodynamic dispersion always creates a transition zone between tracer
marked water and unmarked water. However, if the width of the transition
zone is relatively small in comparison with the study area, the pure advection
model may be adopted without considering the effect of dispersion. This case
may be encountered when the contamination is caused by agriculture, seawater intrusion, artificial rech arge, and so on. As a result, the difficulty in
determining the dispersion coefficient is avoided.
There are two kinds of pure advection models. The first one uses a flow
equation only, and the second one requires coupling of a flow equation with
a quality equation, but without considering the dispersion. They are described below.
1. Solute Transport Prediction with Flow Equation Only
With the transition zone neglected, it is assumed that there is an abrupt
interface between two different bodies of water with different qualities. The
abrupt interface is also called a front, which moves uninterruptedly with the
development of pollution or the transportation of the solute. The problem is
how to determine the location of this moving front. Let us introduce a
numerical method, which is very simple in concept, for solving this problem.
Suppose the location of the front at time t is known and is described by a
set of points on the front. The velocities of these points at moment t can be
calculated by the solution of the flow equation and Darcy's law. Assume that
point i is located at [Xi(t), Yi(t), Zi(t)] at time t, and the components ofvelocity
are l'i,At), l'i,y(t), l'i,Z
{
Xi(t + Ilt) ~ Xi(t) + l'i,At) 'Ilt,
Yi(t + ilt) ~ Yi(t) + l'i,y(t) 'Ilt,
Zi(t + ilt) ~ Zi(t) + l'i,z(t) ·Ilt.
(7.1.15)
When all the locations of these points at t + Ilt are obtained, the approxi-