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Mathematical foundation of Liutex theory

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Abstract

Liutex is a mathematical definition of vortex, which is called the third generation of vortex definition and identification. This paper introduces the mathematical foundation of the Liutex theoretical system including differences in definition and operations between tensor/vector and matrix. The right version of velocity gradient tensor matrix is given to correct the old version which has been widely distributed by many mathematics and fluid dynamics textbooks. A unique velocity gradient principal matrix is provided. The mathematical foundation for Liutex definition is given. The coordinate rotation (Q - and P - rotation) for principal coordinate system and principal matrix is derived, which is the key issue of the new fluid kinematics. The divergence of velocity gradient tensor is given in different forms which may be beneficial in developing new governing equations for fluid dynamics.

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Acknowledgment

The current development of Liutex theory and application is under support by US National Science Foundation (Grant No. 2300052). The authors would like to thank Prof. Lian-di Zhou for the helpful discussions. The authors also would like to thank former UTA team members including Yi-qian Wang, Yi-sheng Gao, Xiang-rui Dong, Jian-ming Liu, Wen-qian Xu and collaborators including Xiao-shu Cai and Hongyi Xu. The authors are thankful to Texas Advanced Computing Center (TACC) for providing the computation hours. The authors would like to thank the University of Texas at Arlington for providing financial support.

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Authors and Affiliations

  1. Department of Mathematics, University of Texas at Arlington, Arlington, Texas, 76019, USA

    Chaoqun Liu & Yifei Yu

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  1. Chaoqun Liu
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  2. Yifei Yu
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Correspondence to Chaoqun Liu.

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Biography: Chaoqun Liu, Male, Ph. D., Professor

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Liu, C., Yu, Y. Mathematical foundation of Liutex theory. J Hydrodyn 34, 981–993 (2022). https://doi.org/10.1007/s42241-023-0091-2

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  • DOI: https://doi.org/10.1007/s42241-023-0091-2

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