Adaptive Mesh Re nement and Multilevel Iteration for Flow inPorous

An adaptive local mesh re nement algorithm originally developed for unsteady gas dynamics by Berger [12, 14] is extended to incompressible ow in porous media. Multilevel iteration and domain decomposition methods are introduced to accommodate the elliptic/parabolic aspects of the ow equations. The algorithm is applied to a two-phase polymer ooding model consisting of a system of nonlinear hyperbolic mass conservation equations coupled to an elliptic pressure equation. While the various numerical methods used have been presented previously, our emphasis is on their consistent combination within the adaptive mesh re nement framework to treat important problems in porous media ow. To achieve e cient, easily maintainable code, we have exploited the features of object-oriented programming for the overall program structure and data management. Examples of algorithmic performance and computational results are provided.