The travel time functional measures the time taken for a particle trajectory to travel from a given initial position to the boundary of the domain. Such evaluation is paramount in the post-closure safety assessment of deep geological storage facilities for radioactive waste where leaked, non-sorbing, solutes can be transported to the surface of the site by the surrounding groundwater. The accurate simulation of this transport can be attained using standard dual-weighted-residual techniques to derive goal-oriented $a$ $posteriori$ error bounds. This work provides a key aspect in obtaining a suitable error estimate for the travel time functional: the evaluation of its G\^ateaux derivative. A mixed finite element method is implemented to approximate Darcy's equations and numerical experiments are presented to test the performance of the proposed error estimator. In particular, we consider a test case inspired by the Sellafield site located in Cumbria, in the UK.
翻译:在封闭后对放射性废物的深地质储存设施进行安全评估时,这种评估至关重要,因为周围地下水可以将渗漏、非吸附、溶液运到现场表面。这种运输的准确模拟可以使用标准的双重加权再生技术,得出目标导向的$a美元误差界限。这项工作为获得对旅行时间功能的适当误差估计提供了一个关键方面:评估其Gáateaux衍生物。对达西的方程式进行了混合限量元素法,并提出了数字实验,以测试拟议误差测算仪的性能。我们特别考虑了英国坎布里亚的Sellafield地点所启发的试验案例。