Conclusions
This book gives a systematic discussion on the theories and methods of
contaminant transport in porous media. Emphases are placed on how to
construct mathematical models and use numerical solutions. Model calibration and model applications are also discussed in certain depth.
To date, however, there are still many open problems in this area. The
author would like to propose the following research subjects to readers who
wish to further study the mathematical modeling of groundwater quality.
1. Probe into the mechanism of hydrodynamic dispersion through la boratory and field experiments, and look for deep understanding of dispersion phenomena in different scales. Thereby, provide theoretical and
experimental bases for improving the existing mathematical models.
2. Study adsorption, ion exchange, and biochemical reactions of different
components in different soils and determine relative parameters.
3. Accurately determine groundwater velocities. One problem is how to
measure them directly in the field. Another problem is how to accurately
determine the hydraulic conductivity K and effective porosity n, then use
Darcy's law to indirectly calculate them. Since indirect calculation is
indispensable in the prediction of water quality changes in a transient
flow field, it is also important to raise the accuracy of calculating gradient
field from the head distribution.
4. Develop efficient numerical solutions for three-dimensional models, because only three-dimensional models can properly describe real cases.
Develop numerical methods for solving the problems of multicomponent
transport in multiphase flow. Establish convenient and applicable software that can solve very large scale problems with the aid of parallel
algorithms.
5. Develop applicable numerical methods that can decrease both numerical
dispersion and overshoot for complicated three-dimensional dispersion
problems.
6. Present new concepts and methods for the parameter identification
of advection-dispersion equations. Quantitatively estimate the model
uncertainty, and study the methods of model validation.
295
This book gives a systematic discussion on the theories and methods of
contaminant transport in porous media. Emphases are placed on how to
construct mathematical models and use numerical solutions. Model calibration and model applications are also discussed in certain depth.
To date, however, there are still many open problems in this area. The
author would like to propose the following research subjects to readers who
wish to further study the mathematical modeling of groundwater quality.
1. Probe into the mechanism of hydrodynamic dispersion through la boratory and field experiments, and look for deep understanding of dispersion phenomena in different scales. Thereby, provide theoretical and
experimental bases for improving the existing mathematical models.
2. Study adsorption, ion exchange, and biochemical reactions of different
components in different soils and determine relative parameters.
3. Accurately determine groundwater velocities. One problem is how to
measure them directly in the field. Another problem is how to accurately
determine the hydraulic conductivity K and effective porosity n, then use
Darcy's law to indirectly calculate them. Since indirect calculation is
indispensable in the prediction of water quality changes in a transient
flow field, it is also important to raise the accuracy of calculating gradient
field from the head distribution.
4. Develop efficient numerical solutions for three-dimensional models, because only three-dimensional models can properly describe real cases.
Develop numerical methods for solving the problems of multicomponent
transport in multiphase flow. Establish convenient and applicable software that can solve very large scale problems with the aid of parallel
algorithms.
5. Develop applicable numerical methods that can decrease both numerical
dispersion and overshoot for complicated three-dimensional dispersion
problems.
6. Present new concepts and methods for the parameter identification
of advection-dispersion equations. Quantitatively estimate the model
uncertainty, and study the methods of model validation.
295