Liutex – The Past, Current, and Future

Speaker: Chaoqun Liu, University of Texas at Arlington
January 30, 2025

Presentation

Abstract

Liutex is a rigorous and mathematical definition of local fluid rotation or vortex, given in 2018 for the first time in history. Liutex is a vector. Liutex direction is the local fluid rotation axis which is defined by the eigenvector of the velocity gradient matrix. Liutex magnitude is twice the local angular rotation speed. The naturally observed vortex core is the concentration of Liutex lines or local maxima of Liutex. Note that natural vortex cores are not vorticity tubes or local maxima of vorticity as defined by almost all fluid dynamics textbooks and countless research papers, which is a historical misunderstanding for almost two centuries. Discovery of Liutex is a groundbreaking work that opens a new era to conduct quantified research on vortex science and turbulence. This is a revolutionary advance in fluid dynamics history. Helmholtz defined vortex as vorticity tubes in 1858, which is classified as the first generation of vortex definition and identification or G1. During the past four decades, many vortex identification criteria including Q, Delta, Lambda 2 and Lambda Ci have been developed, based on the eigenvalues of the velocity gradient tensor matrix, which is classified as the second generation or G2. However, all G2 are scalars but vortex is a vector, and they are strongly dependent on the so-called threshold which is arbitrary and empirical. More seriously, they are all contaminated by shears to different degrees. Therefore, they cannot capture the right vortex structures. After Liutex was born in 2018, many Liutex-based vortex identification methods have been developed and reported, which is called the third generation of vortex identification methods or G3. Among them, the most popular methods are Liutex iso-surface, Liutex-Omega (threshold insensitive), Liutex-core-line (threshold-free and unique), and Objective Liutex, (coordinate system free). According to the Liutex theory, vorticity should be decomposed to a rotational Liutex, and non-rotational shear and velocity gradient tensor should be decomposed to shear, stretching and rotation to replace the classical Helmholtz (Cauchy-Stokes) velocity decomposition. The Liutex similarity in the dissipation sub-region in boundary layers has been found, which could be the foundation for Liutex-based subgrid model for large eddy simulation (LES). Since 2018, thousands of citations in applications of Liutex have been reported and six Liutex books have been published by professional publishers. Six Liutex short courses and workshops have been held. Since the vortex is omnipresent in the universe, the introduction of Liutex will benefit researchers in almost all fluid-related research areas including aerodynamics, hydrodynamics, meteorology, bio flow, space science, etc. Collaborations on hurricanes and tornadoes, sun storms, respiratory flow have been initiated. Two NSF EAGER grants, #2300052 and # 2422573 have been awarded to the UTA Team.

Biography

Chaoqun Liu received both his B.S. and M.S. from Tsinghua University, Beijing, and his Ph.D. from University of Colorado at Denver. He is currently the Tenured and Distinguished Professor and the Director of Center for Numerical Simulation and Modeling at University of Texas at Arlington. He has worked on high order direct numerical simulation (DNS) and large eddy simulation (LES) for flow transition and turbulence for 34 years since 1990. As PI, he has been awarded by the NSF, NASA, US Air Force, and US Navy with 52 federal research grants of over 5.95 million US dollars in the United States. He has published 16 professional books, 144 journal papers, and 170 conference papers and book chapters. He is the founder of Liutex and the third generation of vortex definition and identification methods including the Omega, Liutex, Modified Liutex-Omega, Liutex-Core-Line methods, and Objective Liutex. He is also the founder of Liutex-based new fluid kinematics.