Colloquium- Yuri Bazilevs

Yuri Bazilevs, Vanderbilt University

Stabilized and multiscale methods: unifying cfd for science and engineering

Abstract: After several decades of method development, Computational Fluid Dynamics (CFD) is now considered to be a mature discipline by many. However, as the field grew, the development of CFD methods for basic science applications has taken a different path from that for advanced engineering applications. The development of computational analysis methods for scientific discovery was largely focused on applications that elucidate new scientific phenomena in fluid mechanics, resulting in approaches that often assume simple geometrical configurations, topologically Cartesian grids, and intuitive and easy-to-implement discretizations, such as finite difference methods. The issues of geometric complexity, realistic boundary conditions, topological changes in the problem domain, such as those due to fragmentation or contact, were often secondary and, as a result, were seldom addressed in the method development. Conversely, method development in support of engineering analysis and design was focused on addressing challenges of complex-geometry problem domains, numerical stability of the discretization approaches, and efficiency of the computational procedures. The issues of realistic boundary conditions and problem-domain motion became some of the key drivers for method development, while the fundamental flow physics was often traded for empirical models calibrated for a given application class. 

Given these convergent computational analysis needs for complex unsteady flow problems in science and engineering, a recently proposed variational multiscale (VMS) framework appears to possess the right attributes to be successful in tackling the challenges involved in both. The VMS makes no assumptions about the problem-domain geometry or the flow regime, which makes it attractive for a large class of problems. The variational structure of the VMS enables numerical approximation via standard finite element function spaces or via nonstandard function spaces such as NURBS employed in the Isogeometric Analysis (IGA). The variational structure of VMS is also naturally suited for handling moving-domain problems, and for coupling with solids and structures. The VMS encompasses LES-like turbulence modeling where the small, unresolved scales are accounted for in a consistent fashion in the underlying variational framework.

In this presentation, the VMS framework is developed in the context of Navier—Stokes equations of incompressible flows, and many examples are presented, ranging from classical turbulent-flow test cases, to engineering applications including wind turbines and air vehicles.

Bio: Yuri Bazilevs is a Professor of Civil and Environmental Engineering and of Mechanical Engineering, the J. Lawrence Wilson Chair in Engineering, and the inaugural Director of the SCALES research center at Vanderbilt University. He was the E. Paul Sorensen Professor in the School of Engineering at Brown University, where he was the inaugural Director of the Mechanics of Undersea Science and Engineering (MUSE) center and the Lead and Executive Committee representative of the Mechanics of Solids and Structures group. Yuri’s research interests are in computational mechanics, with emphasis on the modeling and simulation in solids and structures, fluids, and their coupling in HPC environments. For his research contributions Yuri received many awards and honors, including the 2018 Walter E. Huber Research Prize from the ASCE, the 2020 Gustus L. Larson Award from the ASME, the 2022 Computational Mechanics Award from the International Association for Computational Mechanics (IACM), and the 2026 Computational Mechanics Award from the Japan Association for Computational Mechanics (JACM). He is included in the lists of Highly Cited Researchers, both in the Engineering (2015-2018) and Computer Science (2014-2019) categories. Yuri recently completed his service as the President of the US Association for Computational Mechanics (USACM) and as the Chairman of Applied Mechanics Division of ASME. He currently serves as the Vice-Chair of US National Committee for Theoretical and Applied Mechanics (USNC/TAM), the Board of Directors of the USACM, and the Executive Council of the IACM.

Wednesday, September 30, 2026 @ 1:00 p.m.- The Commons Rooms 235/237

Host: Kalman Varga