A Semiclassical Lattice Boltzmann–Ellipsoidal Statistical Method for Hydrodynamics of Quantum Gases

• Main Authors: Po-Chen Tsai, 蔡博臣
• Other Authors: Jaw-Yen Yang
• Format: Others
• Language: zh-TW
• Published: 2013
• Online Access: http://ndltd.ncl.edu.tw/handle/45698888748730622834

碩士 === 國立臺灣大學 === 應用力學研究所 === 101 === A semiclassical lattice Boltzmann–Ellipsoidal Statistical method based on the Uehling-Uhlenbeck Boltzmann-BGK equation and Ellipsoidal Statistical BGK equation is presented. According to gas kinetic theories, the kinetic governing equation for Ellipsoidal Statistical method is directly derived by the Hermite polynomials expansion and lattice velocity model. By using lattice Boltzmann method, this work successfully demonstrates the lid driven cavity flows and Couette flows with different collision operator, BGK and ES-BGK models. Simulations not only shows the similarity and the difference between BGK and ES-BGK collision models but also presents the result for different Reynolds numbers and three quantum particles that obeying Bose-Einstein and Fermi-Dirac and Maxwell-Boltzmann statistics. It is clear to notice that the shapes of the upper upstream secondary eddy of streamlines for three quantum particles from cavity simulation are different between BGK and ES-BGK collision models (the value of b equal -0.5, 0, 0.5), the shape of the upper upstream secondary eddy is more complete as the value of b increases, the shape and position of low pressure center and pressure tensor for three quantum particles from cavity simulations are also different as the value of b is varied. Moreover, simulation for Couette flows not only shows the velocity and temperature distribution but also presents the pressure and pressure tensor contour for three quantum particles. Because ES-BGK collision models (when the value of b equal -0.5) will recover the correct Prandtl number (1→2/3), we also compare our simulations for Maxwell-Boltzmann statistics with exact solution of Couette flows with velocity and temperature difference boundary condition and the result can be found slightly error near the boundary.