Mathematical Sciences: Topics in Applied Mathematics

该项目涉及与石油工程和地球物理相关的应用数学领域的研究。石油工程工作将考虑多孔介质中流动的模拟，特别是包括天然裂隙油藏中的多相流。衰减波可以用双曲型伪微分方程式来描述。大部分研究将致力于发展这种波的数值方法，重点是单相或多相流体饱和的多孔介质中的衰减波；将利用均匀化理论来解释与Biot介质中的慢压缩波有关的散射现象。同样的概念在弹性理论和电磁理论中的应用也将被考虑。将讨论与这些问题有关的几个数值分析问题。这一研究将在结构分析和电磁理论中得到应用。

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.