By combining computational mathematics and several engineering disciplines, a Missouri University of Science and Technology researcher hopes to consistently predict the underground flow of water through porous terrain with large fractures, channels or conduits.

Dr. Xiaoming He, an assistant professor of mathematics and statistics at Missouri S&T, tracks the flow of water and waterborne pollutants as they wash through soil and rocks. He simulates subsurface ground water systems through a three-step process. First, he develops and analyzes a mathematical model, then a numerical method for the simulation. Finally, he collaborates with engineering colleagues to process the porous medium flow in conduits.

“Even though the conduits occupy a small portion of volume in the underground system, they provide a much easier pathway for the water and pollutants than the porous medium,” says He. “Liquids always find the easiest passage out of a pressurized field. My work helps to predict its direction through a field of soil, rocks and fractures.”

His simulations could apply in almost any field where understanding porous medium flow and free flow has an impact. Ground water systems, oil extraction, and industrial filtration are a few of the immediate applications, He says.

“For example, Florida has over 90 percent of its underground water flowing through a ‘Karst aquifer,’ which is a type of subsurface rock that is formed by its own dissolution,” says He. “By tracking the water through this fractured area, we can better predict things such as pollutant transportation.”

He brings smaller-scale portions of the project into the classroom to involve his students in real-world problems, instead of the traditional approach to teaching mathematical equations and formulas. He also believes this will better engage his non-mathematics-majoring students, as the problems combine math with fields such as civil, mining, environmental and petroleum engineering.

“This project provides my undergraduate and graduate students with valuable experiential learning and training opportunities,” says He. “They get to keep in touch with some of the newest developments in mathematical analysis methods and engineering applications, while seeing first-hand how math can be applied in various fields of study.”

His project, titled “Non-Iterative Multi-Physics Domain Decomposition Method for the Navier-Stokes-Darcy Model,” is funded by the National Science Foundation. Dr. Mingzhen Wei, an assistant professor of geosciences and geological and petroleum engineering at Missouri S&T, is the project’s co-investigator.