Diffusion in heterogeneous domains

Speaker’s Name: Professor Vo Anh

Speaker’s Institution: Queensland University of Technology

This work is motivated by the problem of saltwater intrusion in coastal aquifers. These underground aquifers can be a major source of water for irrigation, industrial and town water usage. Due to their proximity to the ocean, excessive demand for groundwater may result in saltwater intrusion with a substantial loss of agricultural land. It is therefore an essential task to develop suitable mathematical models and computational tools for visualisation and prediction of salinity diffusion in aquifers for scenario analysis and management planning.

Due to the complex nature of the aquifers, with alternating layers of permeable sandstone and impermeable clay sediments, it is a challenge to understand the role of heterogeneity in the aquifer and in the physical law governing the saltwater flow. We will formulate the problem in the framework of fractional diffusion in heterogeneous domains. We will outline the existing theory of diffusion on fractals, then move on to a theory of diffusion on multifractals based on the RKHS approach. This latter theory yields a class of models for fractional diffusion with variable singularity order in heterogeneous domains. Wavelet-based expansions of these random fields are employed to obtain finite-dimensional approximations of their linear estimation. A simulation study is presented to illustrate the results.

Seminar Convenors: Andriy Olenko

AGR Contacts: Darren Condon