Topics in Modeling & Numerical Simulation in Applied Mathematics

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DMS-9504556 Douglas The object of this project is to continue the study of the modeling, analysis, and design of parallelizable numerical methods for the simulation of multiphase, multicomponent flow in multilength scale, heterogeneous porous media. Ongoing modeling work focuses on multiphase flow in fractured porous media. The mathematical theory of homogenization will be used in the derivation of new models to describe flow in partially fissured media. Model derivation and parallel software development will be pursued in the context of describing the transport of nuclear waste in fractured porous media. These problems are modeled as single phase, multicomponent flows. The problem of consolidation of clay formations will also be addressed. Both accurate models and numerical methods for the solution of governing systems of equations will be considered. Important applications which will benefit from this work include secondary oil recovery processes, the ecological problem of transport of nuclear waste in groundwater, and the design and analysis of large structures such as dams and multistory buildings. New software packages appropriate for state-of-the-art MIMD machines will be designed and implemented to solve numerically realistic fluid flow problems of the natures described above.