Seminar

To participate in this seminar, please register here: https://www.msri.org/seminars/25657

Contamination of soil and groundwater is a major concern that affects all populated areas. However, this subject is not known for mathematical challenges in fluid dynamics, probably because the dynamics of water in an aquifer is extremely slow. But this slowness is precisely a problem because groundwater pollution can be rapid and its remediation very long. A challenge is therefore to develop models to monitor the vulnerability of aquifers in a context of very heterogeneous time scales.

A large amount of research has been conducted on each of the involved processes (for example, geological, physical, or chemical), so that it may be argued that the corresponding model is already available. Nevertheless, there is such a wide variety of processes (chemical, hydrogeological, and anthropic) acting in such a wide range of temporal and geometrical length scales that the combination of the corresponding model components, if regarded as toolboxes in a software application, is, at best, computationally expensive. And unfortunately, our mathematical skills to manage the corresponding systems of nonlinear, degenerate and strongly coupled pdes are also weak.

In this talk we present some recent developments and open problems for the mathematical handling (modelling, numerical recipes and theory!) of groundwater. We derive and analyse nonlinear moving boundary problems describing the exchanges between the overland and the underground water, saltwater intrusion in coastal areas, agricultural, industrial, or sewage pollution…

Mathematical Modeling of Aquifers