This award supports cooperative research in applied mathematics to be conducted by Jim Douglas of Purdue University and Paulo Jorge S. Paes Leme of the Polytechnic Institute of Rio de Janeiro, Brazil. The objective of the project is to mode., analyze and design numerical methods for the simulation of multiphase flow in a naturally fractured porous medium. The introduction of an appropriate system of differential equations with proper boundary conditions have recently improved various aspects of such flow. For single and two-phase flow this will lead to a better description of the interaction between fluids in fractures and in porous rock. A further goal of this work is to extend this approach to other flows where the effect of compressibility, as well and the interchange of mass between phases is considered. Also, another objective is the study of macroscopic properties of the parameters of these models from microstructural analysis. This award will allow continuation of a productive U.S.-Brazil collaboration.
