Mathematical Modeling and Simulation for Fluid

Mathematical models have been widely used to understand, predict, or optimize many complex physical processes. In particular, simulation of environmental eeects of air polution is extensive. Here we address the need for using similar models to understand the fate and transport of groundwater contaminants and to design in situ remediation strategies. Three basic problem areas must be addressed in the modeling and simulation of the ow of groundwater contamination. One must rst obtain an eeective model to describe the complex uid//uid and uid /rock interactions that control the transport of contaminants in groundwater. This includes the problems of determining and modeling the various multiphase or chemically reactive aspects of the problems which govern the ow of uids, obtaining accurate reservoir descriptions at various length scales, and modeling the eeects of this heterogeneity in the reservoir simulators. Next, one must develop accurate discretization techniques that retain the important physical properties of the continuous models without introducing spurious phenomena related to the discretization errors. Finally, one should develop eecient numerical solution algorithms that utilize the potential of the emerging computing architectures. We will discuss recent advances in each of these three areas.