@Article{CiCP-14-242,
author = {Jaw-Yen Yang, Bagus Putra Muljadi, Zhi-Hui Li and Han-Xin Zhang},
title = {A Direct Solver for Initial Value Problems of Rarefied Gas Flows of Arbitrary Statistics},
journal = {Communications in Computational Physics},
year = {2014},
volume = {14},
number = {1},
pages = {242--264},
abstract = {<p style="text-align: justify;">An accurate and direct algorithm for solving the semiclassical Boltzmann
equation with relaxation time approximation in phase space is presented for parallel
treatment of rarefied gas flows of particles of three statistics. The discrete ordinate
method is first applied to discretize the velocity space of the distribution function to
render a set of scalar conservation laws with source term. The high order weighted essentially non-oscillatory scheme is then implemented to capture the time evolution of
the discretized velocity distribution function in physical space and time. The method
is developed for two space dimensions and implemented on gas particles that obey
the Maxwell-Boltzmann, Bose-Einstein and Fermi-Dirac statistics. Computational examples in one- and two-dimensional initial value problems of rarefied gas flows are
presented and the results indicating good resolution of the main flow features can be
achieved. Flows of wide range of relaxation times and Knudsen numbers covering
different flow regimes are computed to validate the robustness of the method. The
recovery of quantum statistics to the classical limit is also tested for small fugacity
values.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.290112.030812a},
url = {http://global-sci.org/intro/article_detail/cicp/7158.html}
}