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| 1 | Mathematical foundation of Liutex theory显示文摘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. | Chaoqun Liu Yifei Yu | 2022 | Journal of Hydrodynamics2022，34，6： | 4 |
| 2 | Omega-Liutex method for the interaction among wave, current and fixed vertical cylinder显示文摘This paper presents a numerical investigation of the interaction among wave,flow and a fixed cylinder using the naoe-FOAM-SJTU solver,which is a viscous solver for hydrodynamics based on OpenFOAM.The simulation considers the strong nonlinear interaction among a regular wave,flow,and a single fixed cylinder due to viscosity,which is common in offshore structures.The study focus on the vortex induced by viscosity and its significant role in hydrodynamic performance computation.A mesh convergence study is conducted prior to the simulation,and a proper set of mesh is chosen.The simultaneous generation of the regular wave and flow is realized using the numerical field boundary,and the wave propagation is validated.The results of wave elevation and pressures captured by wave gauges and probes around the fixed cylinder are compared with experiment results.The structure of vortices is displayed at significant times,and the phenomena of wave elevation and pressure changes around the cylinder are analyzed in detail using the Omega-Liutex identification method. | Bo Han Zhi Pan Wei-wen Zhao De-cheng Wan | 2023 | Journal of Hydrodynamics2023，35，1： | 0 |
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