Adaptive Mesh Refinement and Multilevel Iteration for Flow in Porous Media

An adaptive local mesh refinement algorithm originally developed for unsteady gas dynamics by M. J. Berger is extended to incompressible flow in porous media. Multilevel iteration and domain decomposition methods are introduced to accommodate the elliptic/parabolic aspects of the flow equations. The algorithm is applied to a two-phase polymer flooding 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 refinement framework to treat important problems in porous media flow. To achieve efficient, 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.

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