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

Ewing9972147 多孔介质中多相污染物的流动和输运等复杂物理现象通常用耦合的非线性偏微分方程组来模拟。 最近在计算能力方面的进展（特别是随着新的并行架构的出现）已经极大地扩展了将更多的物理纳入微分方程的潜力。 虽然这种变化的模型可以提高其能力，以准确地代表潜在的真实的过程，这必须在每个阶段的建模过程中使用物理，数学，数值和计算的概念进行验证。研究员和他的同事开发的分析和数值方法的微分方程描述多相污染物的流动和运输在多孔介质中。 第一个目标是对这些非线性偏微分方程进行理论分析。 特别要处理的主题是正则性，稳定性和分叉现象。 第二个目标是研究和发展能够捕捉尖锐解前沿，产生精确流体速度，保持质量，及时给出高阶近似，在这里，研究人员发展了处理非线性输运扩散方程组的有限元方法，通过欧拉-拉格朗日局部化伴随方法和混合有限元方法，订单时间步进程序。 第三个目标是发展有效的并行迭代求解技术的thegreened离散问题。 该项目继续发展精确的数值技术、有效的计算代码和支持地下水水文学中多相流和输运建模的数学分析，这些技术在修复和清理技术的设计中有应用。 制定更好的方法来评估危险废物对地下水的污染已变得越来越重要。 事实上，地下水供应越来越受到有机、无机和放射性污染物的威胁，这些污染物是通过不适当的处置或意外释放而进入环境的。 据估计，仅美国政府场所的补救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。 也有一些工业应用的建议的研究。 油藏的生产和管理所遵循的方程式和技术与水文学中所采用的方程式和技术几乎相同。 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由与本项目中研究的技术类似的技术控制。 半导体设计所用的方程与地下水输运方程非常相似。 在这些领域，技术转让很容易进行。 特别是，由于它们的知识含量和与工业的密切联系，这些各种各样的问题为学生学习应用和计算数学技术提供了一个很好的工具。

Ewing9972147 Complex physical phenomena involving multiphase contaminantflows and transport in porous media are often modeled by coupledsystems of nonlinear partial differential equations. Recentadvances in computational capabilities (particularly with theadvent of new parallel architectures) have greatly expanded thepotential for incorporating more physics into the differentialequations. While such changes to the model can increase itsability to represent accurately the underlying real process, thismust be verified in each phase of the modeling process utilizingphysical, mathematical, numerical, and computational concepts.The investigator and his colleague develop analytical andnumerical methods for the differential equations describingmultiphase contaminant flows and transport in porous media. Thefirst objective is a theoretical analysis of these nonlinearpartial differential equations. Special topics to be treated areregularity, stability, and bifurcation phenomena. The secondobjective is to study and develop finite element methods capableof capturing sharp solution fronts, producing accurate fluidvelocities, conserving mass, giving high-order approximations intime, and being efficiently adapted in local grid refinement.Here the investigators develop finite element methods fortreating systems of nonlinear transport-diffusion equations viaconcepts of Eulerian-Lagrangian localized adjoint methods andmixed finite element methods coupled with high-ordertime-stepping procedures. The third objective is to developefficient parallelizable iterative solution techniques for theresulting discrete problems. This project continues ongoing development of accuratenumerical techniques, efficient computational codes, andsupporting mathematical analysis for modeling of multiphase flowsand transport in groundwater hydrology that has applications indesign of remediation and clean-up technologies. The developmentof improved methods for assessing groundwater contamination byhazardous wastes has become increasingly important. Indeed,groundwater supplies are increasingly threatened by organic,inorganic, and radioactive contaminants introduced into theenvironment by improper disposal or accidental release. Estimatesof remediation costs at U.S. government sites alone range intothe hundreds of billions of dollars. Protecting the quality ofgroundwater supplies is a grand challenge problem of broadsocietal importance. There are also a number of industrialapplications of the proposed research. The production andmanagment of oil reservoirs are governed by equations andtechnologies that are nearly identical to those exploited ingroundwater hydrology. The manufacture of high quality fiberreinforced plastic composites for automotive and aerospaceapplication is controlled by technology similar to that studiedin this project. Design of semiconductors uses equations veryanalogous to those for groundwater transport. In these areas,technology transfer can be easily carried out. In particular,because of their intellectual content and strong links toindustry, this variety of problems provides an excellent vehiclefor students to learn techniques in applied and computationalmathematics.