This award will support collaborative research between Professor George Pinder of Princeton University and Professor Ismael Herrera of the Universidad Autonoma de Mexico (UNAM) in Mexico City, Mexico. The investigators intend to develop mathematical tools that allow the efficient and accurate simulation of groundwater flow and transport. More specifically, they will design an alternating direction collocation computer code, capable of simulating the movement of multiphase groundwater flow and transport in the subsurface, and programmable for a parallel processor supercomputer. Further, a least squares collocation algorithm will be developed, based upon a total derivative formulation, that will accurately simulate the movement of contaminants exhibiting steep fronts. In addition, the researchers plan to look at boundary element techniques to simulate the movement of non-acqueous phase fluids in the subsurface and carry out a theoretical analysis of the alternation direction collocation algorithm from a functional analysis point of view. Many efforts have been made over the last ten years in devising appropriate numerical methods that can accurately simulate the propagation of sharp fronts in groundwater flow and transport modeling. The proposed work will serve to advance our understanding of such flow problems by combining the theoretical expertise of the Mexican side with the practical experience of the U.S. side in subsurface flow and transport modeling.
