Mathematics researcher earns NSF early-concept exploratory grant

Thursday, Jun 20, 2024 • Greg Pederson :

A researcher in mathematics at The University of Texas at Arlington has been awarded National Science Foundation funding for a project to develop a reliable subgrid model for turbulence in computational fluid dynamics.

Yifei Yu, an assistant professor of research who earned his Ph.D. in mathematics from UTA in 2023, received a two-year, $299,632 Early-Concept Grant for Exploratory Research (EAGER) from the NSF’s Division of Chemical, Bioengineering, Environmental and Transport Systems.

EAGER grants are part of NSF’s early-career researcher funding program. They support exploratory work on untested but potentially transformative research ideas or approaches that are considered high risk and high reward, according to the NSF website.

“I was brimming with joy and excitement when I received the NSF grant,” Yu said. “This grant holds a significant value for me, being the first one I've received as a principal investigator. As a junior research faculty member who only graduated last year, I understand the challenges of acquiring an NSF grant, let alone for someone at the initial stages of their career.”

Chaoqun Liu, UTA professor of mathematics, is co-principal investigator of the grant. The project, titled “EAGER: Liutex-based Sub-Grid Model for Large Eddy Simulation of Turbulent Flow”, focuses on the need to create a better model for small-scale vortices in the study of turbulent flow.

“This is a great achievement for Dr. Yu and Dr. Liu in their research in computational fluid dynamics,” said Jianzhong Su, professor and chair of the UTA Department of Mathematics. “This is an especially important milestone for Dr. Yu to receive an NSF grant as a first-time principal investigator.”

Vortex — the swirling, rotational motion of fluids — is a key factor in turbulence. Vortices are important in the study of natural phenomena including tornadoes, hurricanes, and solar storms as well as in blood flow, aircraft design and many fields of engineering. However, a suitable mathematical definition for vortex had never been developed.

In 2018, Liu and a team of UTA mathematics students formulated a new and unique mathematical definition for vortex, which was first called Rortex and then renamed Liutex by the UTA team and their collaborators in 2019. It correctly represents the pure rigid rotation of fluids and offers a definition that includes information about a vortex’s rotational axis and rotational strength. It distinguishes fluid rotation and shear, a force which influences flow. The discovery of Liutex has been hailed as one of the most important breakthroughs in modern fluid dynamics.

“Vortex is ubiquitous in nature,” Liu wrote in a 2021 book on Liutex which he co-authored. “It is viewed as the building blocks — the muscles and sinews — of turbulent flows.”

This is the second NSF EAGER grant UTA has been awarded for Liutex research in the last two years. In November 2022, Liu received a two-year, $243,229 NSF grant for a project titled “EAGER: Development and Application of Liutex and Third Generation of Vortex Definition and Identification”. The goal of that project is to further modify Liutex to make it unique, accurate, and applicable to vortex science and turbulence research.

“Receiving two EAGER grants in a two-year period shows that NSF believes this work has great potential,” Liu said. “Being able to have a reliable definition of vortex can impact so many areas and can bring advances in meteorology, space science, oceanography, medicine, and many other fields.”

Large eddy simulation (LES) is an important mathematical model for simulating turbulent flow in computational fluid dynamics. It is especially valuable in fields such as aeronautics, automotive engineering, meteorology, bio flow, and space sciences, where understanding how fluids interact with different structures is critical.

“In this (LES) method, large eddies are resolved directly, while smaller scales are modeled,” Yu said. “This approach effectively reduces the demand for computational resources, as small-scale vortices are modeled, thus reducing the need for computation. Therefore, the modeling of small-scale vortices becomes a critical aspect of LES. The focus of our new EAGER project lies in this area, the modeling of small-scale vortices.”

Yu is confident that the use of Liutex will allow for a more refined small-scale vortex model. Existing sub-grid scale models use strain to determine eddy viscosity, which proves inconsistent with the laws of physics due to the nature of shear in the turbulent boundary layers. Yu is confident that a Liutex-based sub-grid scale model will be consistent with physics and thus more reliable and efficient.

Since its introduction in 2018, five books on Liutex have been published by publishing companies including Springer and Elsevier. Six short courses and workshops on Liutex have been held, and another — the International Conference on Liutex-Based Vortex Identification Methods — is scheduled for August 9-11 in Suzhou, China. Liu will be one of the featured speakers.

“The NSF EAGER grants are specifically designed to fund exploratory, high-risk, high-payoff research that has the potential to transform for practical applications,” Yu said. “Therefore, being awarded not just one, but two such grants, indicates that the NSF sees considerable promise and innovative potential in the Liutex research being conducted at UTA. The vortex is a crucial element in fluid dynamics research. This development of Liutex theory could be a monumental advancement, potentially ushering in a new era for quantified research for vortex and turbulence research.”

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