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Numerical algorithms for nonlinear subsurface flow and transport

非线性地下流动和输送的数值算法

基本信息

批准号：
1418752
负责人：
Todd Arbogast
金额：
$ 36.5万
依托单位：
University of Texas at Austin
依托单位国家：
美国
项目类别：
Continuing Grant
财政年份：
2014
资助国家：
美国
起止时间：
2014-07-01 至 2018-06-30
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=1418752&HistoricalAwards=false
关键词：
Numerical algorithms nonlinear subsurface flow

项目摘要

Assessment, design, and monitoring of human activities involving reservoirs and aquifers in the Earth's subsurface require large-scale computer simulation of flow and transport processes over long time periods. Such simulations are used to guide scientists and engineers regarding, e.g., petroleum production, groundwater management, and secure storage of wastes such as carbon dioxide and nuclear contaminants. Computer simulation of the subsurface environment is especially important because it is largely inaccessible to direct observation and therefore also difficult or impossible to rectify human failures. The project involves fundamental research and education on immiscible, two-phase subsurface flow. This project has the potential for significantly greater fidelity simulations by properly accounting for the nonlinearly coupled behavior of the physical processes embodied in the governing equations, and the numerical algorithms should work well on modern supercomputers. Moreover, many models of scientific and engineering interest consist of similar nonlinearly coupled flow and transport systems, and so general progress here is likely to support efforts more broadly. The project will fund the research of two STEM Ph.D. graduate students and involve at least two undergraduate students. They will work in the Center for Subsurface Modeling of the Institute for Computational Engineering and Sciences, which provides an interdisciplinary environment mixing expertise in mathematics, computational science, petroleum engineering, and geological science. The students will be prepared for employment opportunities in academia, government laboratories, and industry. External collaborations will enhance the impact of the project.The project involves fundamental research on and development of new algorithms for nonlinear, coupled systems of partial differential equations with algebraic constraints. The target system to be addressed is immiscible, two-phase subsurface flow, which is used for numerical simulation of the movement of underground fluids. The project emphasizes the highly nonlinear physical processes of flow and transport, and how they influence each other. The objectives of the project are: (1) Improved numerical algorithms of mixed type for approximation of nonlinear flow within a multi-scale, heterogeneous porous medium when coupled to a transport model; (2) Development of Eulerian-Lagrangian Weighted Essentially Non-Oscillatory numerical algorithms for multi-dimensional, nonlinear transport when coupled to a nonlinear flow model; (3) Demonstration of the effectiveness of the algorithms in specific applications such as petroleum production, groundwater management, and carbon sequestration; and (4) Education and training of two graduate and two undergraduate students in an interdisciplinary setting. The project is expected to result in significantly better numerical approximations of subsurface flow and transport, even over very long time periods. Project success will be seen by the development of numerical algorithms that preserve mass locally, produce little to no overshoots or undershoots, exhibit low levels of numerical diffusion, and are of high order and accurate on coarse computational meshes. They will require a significantly relaxed CFL time-step restriction for stability. Most importantly, the methods will be shown to work well for the nonlinearly coupled system, in that the two systems will complement each other in terms of accuracy and efficiency.

评估、设计和监测涉及地球地下水库和含水层的人类活动，需要对长时间的流动和运输过程进行大规模计算机模拟。这种模拟用于指导科学家和工程师，例如，石油生产、地下水管理以及二氧化碳和核污染物等废物的安全储存。地下环境的计算机模拟特别重要，因为它在很大程度上无法直接观察，因此也很难或不可能纠正人为失误。该项目涉及不混溶两相地下流的基础研究和教育。这个项目有潜力显着更高的保真度模拟适当占的非线性耦合行为的物理过程中体现的控制方程，数值算法应该在现代超级计算机上工作得很好。此外，许多具有科学和工程意义的模型都由类似的非线性耦合流动和输运系统组成，因此这里的一般进展可能会更广泛地支持这些努力。该项目将资助两名STEM博士的研究。研究生，并涉及至少两名本科生。他们将在计算工程与科学研究所的地下建模中心工作，该中心提供了一个跨学科的环境，混合了数学，计算科学，石油工程和地质科学的专业知识。学生将准备在学术界，政府实验室和工业的就业机会。外部合作将加强该项目的影响，该项目涉及对具有代数约束的非线性、耦合偏微分方程系统进行基础研究并开发新算法。要解决的目标系统是不混溶的，两相地下流动，这是用于地下流体的运动的数值模拟。该项目强调流动和运输的高度非线性物理过程，以及它们如何相互影响。该项目的目标是：（1）改进混合型数值算法，用于与输运模型耦合时多尺度、非均匀多孔介质内非线性流动的近似;（2）发展欧拉-拉格朗日加权基本无振荡数值算法，用于与非线性流动模型耦合时多维、非线性输运;（3）算法在石油生产，地下水管理和碳封存等具体应用中的有效性的演示;（4）在跨学科环境中对两名研究生和两名本科生进行教育和培训。该项目预计将导致显着更好的数值近似的地下水流和运输，即使在很长的时间段。项目的成功将通过数值算法的开发来实现，这些算法可以局部保持质量，几乎不产生过冲或下冲，表现出低水平的数值扩散，并且在粗糙的计算网格上具有高阶和准确性。他们将需要一个显着放宽CFL的时间步长限制的稳定性。最重要的是，该方法将被证明是工作良好的非线性耦合系统，在这两个系统将相互补充的精度和效率。