Modeling Rarefied Gas Flows of Arbitrary Statistics with the Semiclassical Boltzmann-BGK equation
Date Issued
2015
Date
2015
Author(s)
Diaz, Manuel A.
Abstract
The semiclassical Boltzmann equation is a generalization of the classical Boltzmann Equation intended to describe the dynamics of quantum particle system in phase space. Originally formulated by Nordheim in 1928 and extended by Uehling and Uhlenbeck in 1933, it is a suitable mathematical model capable of describing classical and quantum gases under a single framework. This general framework although simple it is not simplistic and possess many numerical challenges due to the non-linear quantum relations that arise in it. Although many approaches to model the hydrodynamic of quantum systems have been reported throughout the literature, the non-linear nature of the quantum thermodynamic relations hinders many methodological opportunities. This is especially true when considering conditions where the quantum effects play a major role, the near-degenerate regimes. In this dissertation, a new numerical methodology is presented to solve the Boltzmann-BGK equation of gas dynamics for the classical and quantum gases described by the Bose-Einstein and Fermi-Dirac statistics. Moreover, an efficient direct solver based on discontinuous polynomial representation is investigated to explore the parallel computing opportunities in modeling quantum gas systems. In this work, the proposed numerical methodology is validated by benchmark problems of gas dynamics. Descriptions of ideal quantum gases including internal degrees of freedom are successfully achieved and reported for the first time.
Subjects
Quantum Hydrodynamics
Flux Reconstruction
Quantum Boltzmann Equation
Type
thesis
File(s)![Thumbnail Image]()
Loading...
Name
ntu-104-F99543083-1.pdf
Size
23.54 KB
Format
Adobe PDF
Checksum
(MD5):25dd0541efe7307b89573bf40640d238