The objective of the proposed project is to accurately model complex flow and transport phenomena arising in groundwater contamination and in sepsis modeling.
Groundwater forms two-thirds of the world's fresh water. This resource, vital to human activities, is constantly threatened by contamination. Groundwater becomes contaminated when man-made and sometimes naturally-occurring substances are dissolved in waters recharging the groundwater. Often, as groundwater is connected with lakes and rivers, the pollution of these surface waters implies the pollution of aquifers. Thus, it is important to understand the flow and transport of the coupled system of rivers, lakes, and aquifers. In this first application, such complex multiphysics couplings are studied.
The second application modeled in this work involves sepsis, which in the U.S. is the primary cause of death in critically ill patients. Sepsis can be defined as an uncontrolled inflammatory response due to bacterial infection. As of today, there are very few therapeutic options available to patients. Simulating inflammation and organ dysfunction that accompany sepsis can help understand this complex problem. The modeling process consists of identifying key chemical components and their interaction in different subdomains such as organs, epithelial layers, and blood arteries.
The underlying mathematical equations characterizing both applications are similar. Those equations are derived from the balance equations of continuum mechanics that express the conservation laws for mass, momentum, and energy of an arbitrary volume moving within a fluid. Efficient and reliable numerical methods will be developed as a part of this project. One project output will be a computational tool that is beneficial to both environmental engineers and medical personnel. On one hand, effective strategies for clean-up of contaminated groundwaters can be simulated. At the same time,a better understanding of the inflammatory response due to bacterial infection will lead to the design of therapeutic solutions for sepsis. Another impact of this project will be the stimulation of the discovery process for undergraduate and graduate students involved in the research project.
Educational activities for the proposed project include the development of a new modeling course, the creation of a Master's degree in Computational and Applied Mathematics, the continuous mentorship of graduate and undergraduate students and their exposure to international collaborations, and an increase in the number of students, including minorities, graduating with a Master or Ph.D. degree in Mathematics.
