Mathematical modeling and simulation for fluid flow in porous media

Mathematical models have been widely used to understand, predict, or optimize many complex physical processes. In particular, simulation of environmental effects 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 flow of groundwater contamination. One must first obtain an effective model to describe the complex fluid/fluid and fluid/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 flow of fluids, obtaining accurate reservoir descriptions at various length scales, and modeling the effects 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 efficient numerical solution algorithms that utilize the potential of the emerging computing architectures. We will discuss recent advances in each of these three areas.