William J. Layton

Dr. Layton's research develops novel algorithms, models and analysis aiming to understand fluid motion.  For example, one central challenge is in modeling the large eddies (such as storm fronts, hurricanes, and tornadoes in the atmosphere) in turbulent flow, predicting their motion in computational experiments and validating mathematically the large eddy models and algorithms developed. This need led to the development of large eddy simulation as a field of computational science. Dr. Layton’s group developed the mathematical foundations of how LES models work, when they fail and how their accuracy is to be understood and studied. One recent development is the design of the first ensemble algorithms that push out the predictability horizon in chaotic systems. This is essential for time-accurate predictions of fluid motion, a central research theme of the group. 

Another current challenge is to develop new mathematical tools (algorithms with theory) for studying flow and contaminant transport between surface and ground water. The fundamental paper in the area arises from work with colleague Ivan Yotov and the first effective partitioned methods were designed by PhD students of the group. Other partitioned methods were developed for coupled, multi-physics systems including coupling atmosphere models and ocean models in climate studies.