Article

Lattice Uehling-Uhlenbeck Boltzmann-Bhatnagar-Gross-Krook hydrodynamics of quantum gases.

Center for Quantum Science and Engineering, National Taiwan University, Taipei 106, Taiwan.
Physical Review E (impact factor: 2.26). 06/2009; 79(5 Pt 2):056708. pp.056708
Source: PubMed

ABSTRACT We present a semiclassical lattice Boltzmann method based on quantum kinetic theory. The method is directly derived by projecting the Uehling-Uhlenbeck Boltzmann-Bhatnagar-Gross-Krook 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. Gases of particles of arbitrary statistics can be considered. Simulation of one-dimensional compressible gas flow and two-dimensional hydrodynamic flows are shown. The results indicate distinct characteristics of the effects of quantum statistics.

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Keywords

arbitrary statistics
 
Gauss-Hermite quadrature
 
Grad's moment expansion method
 
intrinsic discrete nodes
 
natural lattice velocities
 
one-dimensional compressible gas flow
 
quantum statistics
 
semiclassical lattice Boltzmann method
 
two-dimensional hydrodynamic flows
 
Uehling-Uhlenbeck Boltzmann-Bhatnagar-Gross-Krook equations