Mathematical Sciences: Topics in Applied Mathematics

数学科学：应用数学专题

• 批准号: 9207088
• 负责人: Jim Douglas
• 金额: $ 20.25万
• 依托单位: Purdue Research Foundation
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1992
• 资助国家: 美国
• 起止时间: 1992-07-15 至 1995-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9207088&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Topics; Applied; Mathematics

This project involves research in the areas of applied mathematics related to petroleum engineering and geophysics. The petroleum engineering work will consider simulation of flows in porous media, including, in particular, multiphase flow in naturally fractured petroleum reservoirs. Attenuated waves are best described by means of hyperbolic pseudo-differential equations. Much of the research will be devoted to developing numerical methods for such waves, with emphasis on attenuated waves in porous media saturated by single- or multiphase fluids; interpretation of scattering phenomena related to the slow compression wave in Biot media will be studied by means of homogenization theory. Applications of the same concepts in elasticity theory and electromagnetic theory will be considered. Several numerical analysis questions related to these problems will be treated. This research will have applications in structural analysis and electromagnetic theory.

该项目涉及应用领域的研究 与石油工程和地球物理学有关的数学。 的 石油工程工作将考虑模拟流动， 多孔介质，特别是多相流， 天然裂缝油气藏 衰减波是 最好用双曲伪微分来描述 方程 大部分研究将致力于开发 这种波的数值方法，重点是衰减 单相或多相流体饱和的多孔介质中的波; 与慢波相关的散射现象的解释 本文将用数值方法研究毕奥介质中的压缩波 均质化理论 相同概念在以下方面的应用 将考虑弹性理论和电磁理论。 与这些问题相关的几个数值分析问题 将得到治疗。 这项研究将在结构分析中得到应用 电磁理论。