摘要
Classical fluid kinematics or Cauchy-Stokes decomposition mistreated vorticity as fluid rotation and mixed flow stretching with shearing.Classical fluid dynamics or Navier-Stokes(N-S)equations are based on the classical kinematics and treated vorticity as null in contribution of forces and mixed the stretching force with the shearing force,which is not consistent with the Galilean invariancy.N-S equations also neglect the flow rotation.It is believed that N-S equations may work for incompressible and laminar flow but are not satisfied for turbulent flow and compressible flow especially for high-speed flow.Based on Liutex,new fluid kinematics has been established by Liu in 2021,which gives a Liutex-based principal coordinate system and a new principal decomposition in that system,which has been transferred back to the original Cartesian coordinate system.The principal decomposition of velocity gradient tensor has four parts which are called rotation,stretching,anti-symmetric shearing and symmetric shearing.Four forces are derived according to the four parts of the velocity gradient tensor.According to the new fluid kinematics,it is reported in this letter that based on the principal decomposition,a new relation between the velocity gradient tensor and stress-rate tensor has been established to form a new fluid dynamics equation to govern fluid flow.The new governing equation may be applicable to both laminar flow and turbulent flow,and both incompressible flow and compressible flow including high-speed flow for reasonable results with reasonable grids.Further numerical experiment is needed to verify.
基金
This work was mainly supported by the Department of Mathematics of University of Texas at Arlington as the author is the full-time professor in UTA and all students and visitors were housed by UTA。
