Topics in Modeling & Numerical Simulation in Applied Mathematics

DMS-9504556道格拉斯这个项目的目标是继续研究可并行数值方法的建模、分析和设计，以模拟多长度尺度、非均匀多孔介质中的多相、多组分流动。正在进行的建模工作主要集中在裂隙多孔介质中的多相流。在推导描述部分裂隙介质中渗流的新模型时，将使用均化的数学理论。将在描述核废料在裂隙多孔介质中的运输的背景下进行模型推导和并行软件开发。这些问题被建模为单相、多组分的流动。此外，亦会讨论粘土地层的固结问题。本课程将同时考虑求解控制方程组的精确模型和数值方法。将从这项工作中受益的重要应用包括石油二次回收过程、在地下水中运输核废料的生态问题，以及大坝和多层建筑等大型结构的设计和分析。将设计和实施适用于最先进的MIMD机器的新软件包，以解决上述性质的数值现实流体流动问题。

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.