Mathematical Modeling and Simulation for Applications of Fluid Flow in Porous Media

Mathematical models have been widely used to understand, predict, or optimize many complex physical processes. Here we address the need for developing 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 effective model equations to describe the complex fluid/fluid and fluid/rock interactions that control the transport of contaminants in groundwater. This includes the problem of obtaining accurate reservoir descriptions at various length scales, modeling the effects of this heterogeneity of the porous medium, and developing effective parameters in the governing models that describe the effects of the heterogeneities in the reservoir simulators. Next, one must develop accurate discretization techniques that retain the important physical properties of the continuous models. Finally, one should develop efficient numerical solution algorithms that utilize the potential of the emerging computing architectures. We will discuss advances in these areas.