Professor Borggaard studies the design and control of fluids. This includes computational fluid dynamics, control theory, optimization, sensitivity analysis, uncertainty quantification, and reduced-order models. In each case, the application of these research areas to partial differential equations that describe fluids are of interest.
Professor Chung's research concerns computational methods in the intersection of computational modeling, machine learning, data analytics with an emphasis on inverse problems. Driven by its application, he and his group develop and analyze efficient numerical methods for inverse problems. Applications of interest are, but not limited to, systems biology, medical and geophysical imaging, and dynamical systems.
At the core of Professor Iliescu's research program is his vision of using both mathematics and computations to provide new knowledge on turbulent fluid flows dominated by coherent structures and create models with practical impact in engineering, climate modeling, and medicine. The ultimate goal of his research program is to transform turbulence modeling as we know it today and use mathematics, computations, physics, and data to discover general laws of turbulent fluid flows.
Professor Tao Lin's main research interest is the numerical analysis on computational methods related with differential equations. He designs new numerical methods and carry out their convergence analysis. His recent research focuses on immersed finite element (IFE) methods that can solve interface problems of partial differential equation with interface independent meshes. He is also working on applying IFE methods to interface inverse problems via the shape optimization methodology.
Professor Wapperom conducts research in computational fluid dynamics of complex fluids. This involves the mathematical modeling and numerical simulation of the flow of polymeric liquids and fluids reinforced with rigid particles.
Professor Warburton holds the John K. Costain Chair in the College of Science at Virginia Tech and is a faculty member of both the Department of Mathematics and the Computational Modeling and Data Analytics program. His research interests include developing new parallel algorithms and methods that are used to solve PDE based physical modes on the largest supercomputers.
Professor Yue works on the numerical simulation of flow problems with moving boundaries and complex rheology, including multiphase flow, viscoelastic fluids, dynamic wetting, and phase change phenomena.