@Article{AAMM-7-2,
author = {Songze, Chen and Xu, Kun and Qingdong, Cai},
title = {A Comparison and Unification of Ellipsoidal Statistical and Shakhov BGK Models},
journal = {Advances in Applied Mathematics and Mechanics},
year = {2015},
volume = {7},
number = {2},
pages = {245--266},
abstract = {<p style="text-align: justify;">The Ellipsoidal Statistical model (ES-model) and the Shakhov model (S-model)
were constructed to correct the Prandtl number of the original BGK model
through the modification of stress and heat flux. With the introduction of a new parameter
to combine the ES-model and S-model, a generalized kinetic model can be
developed. This new model can give the correct Navier-Stokes equations in the continuum
flow regime. Through the adjustment of the new parameter, it provides abundant
dynamic effect beyond the ES-model and S-model. Changing the free parameter,
the physical performance of the new model has been tested numerically. The unified
gas kinetic scheme (UGKS) is employed for the study of the new model. In transition
flow regime, many physical problems, i.e., the shock structure and micro-flows, have
been studied using the generalized model. With a careful choice of the free parameter,
good results can be achieved for most test cases. Due to the property of the Boltzmann
collision integral, the new parameter in the generalized kinetic model cannot
be fully determined. It depends on the specific problem. Generally speaking, the S-model
predicts more accurate numerical solutions in most test cases presented in this
paper than the ES-model, while ES-model performs better in the cases where the flow
is mostly driven by temperature gradient, such as a channel flow with large boundary
temperature variation at high Knudsen number.</p>},
issn = {2075-1354},
doi = {https://doi.org/10.4208/aamm.2014.m559},
url = {https://global-sci.com/article/73394/a-comparison-and-unification-of-ellipsoidal-statistical-and-shakhov-bgk-models}
}