Particle Tracking

Tracking particles through a moving field, such as flowing air, ground, or surface water, is not only a powerful computational method but can also provide insightful visualizations. I have employed this process for a variety of problems from airborne contamination, thermal pollution, and contaminant transport in groundwater. I have even used it to successfully model the mixing of fluorescent dye through the confluence of three pumps in order to distinguish the time of arrival at the destination. While the Lagrangian method (based on time as the independent parameter) is most often used, the Hamiltonian method (based on time as a dependent parameter) can be much faster. Both are developed in this text, which includes many examples. Diffusion (spreading based on material properties) and also dispersion (based on local velocities) are derived, implemented, and illustrated in the text. Flow in factures within porous media, essential to accurately modeling karst formations, is also covered.