Hybrid numerical-analytical methods for subsurface flow simulation

许多地下环境/水资源问题非常复杂，需要数学模型来理解它们，并为管理者和决策者提供指导。21世纪初的重大地下模拟问题，如确定碳封存工作的泄漏风险，保护河流和地下水免受交叉污染，或验证页岩气水力压裂对环境的影响，可能会因当前建模技术的计算缺陷而受到阻碍。有些问题是现有技术根本无法解决的，有些问题只能用超级计算机来解决。如果要将模型用于风险分析或管理优化，则需要更快和更合适的数值方法，这两种方法都需要单个模型运行数千次。如果不改进这项技术，我们就无法测试有关水资源管理和保护的关键“假设”情景，这可能会使我们面临潜在的严重公共卫生后果的风险。在布鲁斯半岛拟议的核废料储存库等案例中，使用缓慢或不准确的地下模型可能严重限制我们以可靠的科学为环境政策决策提供适当信息的能力。

Many subsurface environmental / water resources problems are intensely complex, and mathematical models are required to both understand them and to provide guidance to managers and policymakers. Significant subsurface simulation problems of the early 21st century, such as determining leakage risk from carbon sequestration efforts, protecting rivers and groundwater from cross-contamination, or verifying the environmental impact of hydraulic fracturing for shale gas, are likely to be handicapped by the computational shortcomings of current modelling techniques. There are certain problems which simply can't be solved with current technology, others which can only be solved with supercomputers. Faster and more appropriate numerical methods are desirable if the models are to be used for risk analysis or management optimization, both of which require a single model to be run perhaps thousands of times. Without improvements to the technology, we are unable to test critical 'what if' scenarios regarding the regulation and protection of our water resources, which can put us at risk of potentially serious public health consequences. In cases such as the proposed nuclear waste repository on the Bruce peninsula, the use of slow or inaccurate subsurface models can seriously limit our ability to properly inform environmental policy decisions with sound science. This research program intends to address some of the more salient limitations of standard modelling approaches by developing and applying novel mathematical techniques that marry conventional discrete methods with special closed-form analytical solutions. These new methods will initially be developed with application to systems with intimate groundwater-surface water connections, complementing current research by the primary investigator into numerical methods for simulating subsurface geoexchange systems and influences of pumping on streams and wetlands. These fundamental advances will, in the long term, help to improve our ability to predict and assess the impact of our environmental policies.