Mixed finite element approximation of porous media flows - Rourke, Fran (2023)
The reliable simulation of flow in fractured porous media is a key aspect in the decision making process of stakeholders within politics and the geosciences, for example when assessing the suitability of burial sites for storage of high–level radioactive waste. This thesis aims to tackle the challenge that is the accurate simulation of these flows and does so via three computational developments. That is, suitable models for porous media flow with fractures; obtaining rigorous and reliable estimates of errors generated through these models; and the accurate simulation of the times–of–flight for particles transported by groundwater within the porous medium. Firstly, an expansion procedure for fractures in porous media is developed so that physical fluid laws are still retained when tracking particles across fracture–bulk interfaces. Moreover, the second contribution of this work is the utilisation of the dual–weighted–residual method to define suitable elementwise indicators for generic quantities of interest. The third contribution of this thesis is the attainment of accurate simulations of travel times for particles in porous media, achieved through linearising the functional representing the time–of–flight; in practice, numerical examples, including one inspired by the Sellafield site in Cumbria, UK, validate the performance of the proposed error estimator, and hence are useful in the safety assessment of storage facilities intended for radioactive waste.