Karst aquifiers represent a very significant source of water for public and private use. A Karst aquifer, in addition to a porous limestone matrix, typically has large cavernous conduits that are known to largely control groundwater flow and contaminant transport within the aquifer. We will develop a new modeling approach for water flow and contaminant transport in conduit/matrix systems. The flow in the conduits will be described by the Navier-Stokes equations and that in the matrix by Darcy's law. Convection-diffusion equations are used to describe the solute transport in the two regions. The conditions applied at the conduit/matrix interface are novel. We will subject the new Navier-Stokes/Darcy model to rigorous mathematical analyses, studying such issues as existence of solutions and continuous dependence on data. This represents the first such study of this kind. Analyses will also be used to take advantage of the multiscale character of flows in Karst aquifiers to derive fully justified model simplifications that will result in less costly computational algorithms. We will also develop mixed Galerkin and least-squares finite element methods for the coupled Navier-Stokes/ Darcy model along with a coupled convection-diffusion model for the transport of contaminants. Experiments will be a crucial aspect of the proposed project. They will be used to obtain information about flows and contaminant migration in conduit/matrix systems that can not only be useful to water resource managers and policy makers, but also for the development and validation of mathematical models and computational algorithms.
Certainly, advances in our quantitative knowledge of Karst aquifers will greatly help in their administration, including the delineation of source-water protection areas for public water supplies and the design of monitoring programs to evaluate the residence and fate of contaminant plumes. More generally, the methodologies we will produce can also impact other underground fluid flow problems including some arising in the petroleum industry. The proposed project will provide a vehicle for the bona fide interdisciplinary training of students and postdoctoral researchers. They will gain the ability to make accurate quantitative assessments of aquifiers and thus can provide industrial administrators and governmental officials with the information they need to make sound policy decisions.
