Mathematical Sciences: Innovative Finite Element Methods for Modeling Multiphase Contaminant Flows in Porous Media

9626179 Ewing与地下水模拟、污染物地下运移和油藏模拟有关的多孔介质中的流体流动模拟需要非线性时变偏微分方程的大型耦合系统的数值逼近。发展有效的大规模模拟数值技术对于理解这些多孔介质的流动是非常重要的。由于耦合微分系统中的波状或行前问题和高度局域性以及许多油藏模拟问题的巨大规模，高效数值模拟的一个重要目标是能够有效地模拟这些影响并利用新的超级计算机体系结构。该项目将集中发展有限元方法、计算代码和支持地下污染流的数学分析。数值方法将被设计用来模拟流体的复杂特征，如激波线饱和锋和陡峭的成分梯度，以产生精确的流体速度，局部保存质量，并利用新的并行超级计算机。研究了大型线性系统迭代解的自适应局部网格细化方法和有效实现技术。提出了一项为期三年的研究计划，旨在发展精确的数值技术，有效的计算代码，以及支持地下水水文多相流和运输建模的数学分析，并在修复和清理技术的设计中应用。发展评估危险废物对地下水污染的改进方法已变得日益重要。事实上，地下水供应正日益受到有机、无机和放射性污染物的威胁，这些污染物是由于处置不当或偶然的牙科释放而进入环境的。据估计，仅美国政府垃圾场的修复费用就高达数千亿美元。保护地下水供应的质量是一个具有广泛社会重要性的重大挑战问题。所提出的研究也有许多工业应用。油藏的生产和管理是由方程式和技术控制的，这些方程式和技术几乎与地下水水文学中所开发的相同。用于汽车和航空航天应用的高质量纤维增强塑料复合材料的制造是由类似于本项目研究的技术控制的。半导体的设计使用的方程与地下水输送的方程非常相似。在这些领域，可以很容易地进行技术转让：使用为此开发的代码，与研究人员进行工业合作，并雇用受过该项目的培训的学生。

9626179 Ewing The simulation of fluid flow in porous media related to groundwater modeling, subsurface transport of contaminants, and petroleum reservoir simulation requires the numerical approximation of large coupled systems of nonlinear time-dependent partial differential equations. The development of efficient numerical techniques for the large-scale simulation is extremely important in understanding these porous media flows. Due to wave-like or traveling front problems and highly localized natures in the coupled differential systems and the enormous size of many reservoir simulation problems, an important goal of efficient numerical modeling is the ability to effectively model these effects and the utilization of new supercomputer architectures. This project will concentrate on the development of finite element methods, computational codes, and supporting mathematical analysis for underground contamination flows. The numerical methods will be designed to simulate such complex features of the flows as shock-line saturation fronts and steep composition gradients, to produce accurate fluid velocities, to conserve mass locally, and to take advantage of new parallel supercomputers. Self-adaptive local grid- refinement methods and efficient implementation techniques for iterative solution of large linear systems are also studied. A three-year program of research is proposed into the development of accurate numerical techniques, efficient computational codes, and supporting mathematical analysis for modeling of multiphase flows and transport in groundwater hydrology which has applications in design of remediation and cleanup technologies. The development of improved methods for assessing groundwater contamination by hazardous wastes has become increasingly important. Indeed, groundwater supplies are increasingly threatened by organic, inorganic, and radioactive contaminants introduced into the environment by improper disposal or acci dental release. Estimates of remediation costs at U.S. government sites alone range into the hundreds of billions of dollars. Protecting the quality of groundwater supplies is a grand challenge problem of broad societal importance. There are also a number of industrial applications of the proposed research. The production and management of oil reservoirs are governed by equations and technologies that are nearly identical to those exploited in groundwater hydrology. The manufacture of high quality fiber reinforced plastic composites for automotive and aerospace applications is controlled by technology similar to that studied in this project. Design of semiconductors uses equations very analogous to those for groundwater transport. In these areas, technology transfer can be easily carried out: use of the codes developed for, industrial collaboration with the researchers of, and employment of students trained on this project.