Semiclassical Lattice Boltzmann Method
Date Issued
2010
Date
2010
Author(s)
Hung, Li-Hsin
Abstract
Unlike describing the physical phenomenon in coordinate or momentum spaces in quantum mechanics, semiclassical Boltzmann equation treats the system in phase space, and it is much easier to describe the dynamics of quantum gases. In this thesis, a class of semiclassical lattice Boltzmann methods is developed for solving quantum hydrodynamics and beyond. The present method is directly derived by projecting the Uehling-Uhlenbeck Boltzmann-BGK equations onto the tensor Hermite polynomials following Grad''s moment expansion method. The intrinsic discrete nodes of the Gauss-Hermite quadrature provide the natural lattice velocities for the semiclassical lattice Boltzmann method. Formulations for the second-order and third order expansion of the semiclassical equilibrium distribution functions are derived and their corresponding hydrodynamics are studied. Gases of particles of arbitrary statistics can be considered. Simulations of one-dimensional compressible gas flow by using D1Q5 lattices, two dimensional microchannel flow, two dimensional flow over cylinder by using D2Q9 lattices and three dimensional lid driven cavity flow by using D3Q19 lattices are provided for validating this method. It is shown that the classical flow patterns such like vortex and vortices shedding in flow over cylinder simulations, temperature and pressure contours together with streamline patterns could be produced from the present method in classical limit. The results also indicate the distinct characteristics of the effects of quantum statistics when they are compared with fluid phenomena in classical statistics.
Keywords: Lattice Boltzmann Method, Semiclassical, Quantum.
Subjects
Lattice Boltzmann Method
Semiclassical
Quantum
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