| Summary: | 碩士 === 國立臺灣大學 === 應用力學研究所 === 102 === Modeling gases in the continuum level is traditionally achieved with macroscopic level by using Euler or Navier-Stokes equations. However, as the degree of rarefaction of a gas increses, the governing equation becomes Boltzmann Equation. The Lattice Boltzmann method is derived by discretizing Boltzmann equation in physical and velocity space.
In the study, the development of a semiclassical lattice Boltzmann–Ellipsoidal Statistical method is based on the Uehling-Uhlenbeck Boltzmann-BGK equation. According to the method, we can effectively link its dominant distribution function to calculate the quantities of macroscopic properties. Here, we present simulations of the flow over cylinder for several Reynolds numbers based on D2Q9 lattice model and the semiclassical lattice Boltzmann–Ellipsoidal Statistical method. In this work, the Immerse Boundary Velocity Correction method (IBVCM) has been used to model the boundary of the cylinder. We compare the results of vortices, pressure, drag coefficient for different particle statistics : Bose-Einstein, Fermi-Dirac and Maxwell-Boltzmann statistics. By studying the streamlines, we observed von Karman vortex street phenomenon as the Reynolds number increases. In addition, the movement of the cylinder boundary is not stationary in the flow channel by taking advantage of the boundary using IBVCM. We observed the wake and found differences in the results of the three statistics.
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