Numerical algorithms for nonlinear subsurface flow and transport

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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.