@Article{CiCP-12-662,
author = {Juan-Chen Huang, Kun Xu and Pubing Yu},
title = {A Unified Gas-Kinetic Scheme for Continuum and Rarefied Flows II: Multi-Dimensional Cases},
journal = {Communications in Computational Physics},
year = {2012},
volume = {12},
number = {3},
pages = {662--690},
abstract = {<p style="text-align: justify;">With discretized particle velocity space, a multi-scale unified gas-kinetic
scheme for entire Knudsen number flows has been constructed based on the kinetic
model in one-dimensional case [J. Comput. Phys., vol. 229 (2010), pp. 7747-7764]. For
the kinetic equation, to extend a one-dimensional scheme to multidimensional flow is
not so straightforward. The major factor is that addition of one dimension in physical
space causes the distribution function to become two-dimensional, rather than axially
symmetric, in velocity space. In this paper, a unified gas-kinetic scheme based on the
Shakhov model in two-dimensional space will be presented. Instead of particle-based
modeling for the rarefied flow, such as the direct simulation Monte Carlo (DSMC)
method, the philosophical principal underlying the current study is a partial-differential-equation (PDE)-based modeling. Since the valid scale of the kinetic equation and
the scale of mesh size and time step may be significantly different, the gas evolution in a discretized space is modeled with the help of kinetic equation, instead of
directly solving the partial differential equation. Due to the use of both hydrodynamic and kinetic scales flow physics in a gas evolution model at the cell interface,
the unified scheme can basically present accurate solution in all flow regimes from
the free molecule to the Navier-Stokes solutions. In comparison with the DSMC and
Navier-Stokes flow solvers, the current method is much more efficient than DSMC in
low speed transition and continuum flow regimes, and it has better capability than
NS solver in capturing of non-equilibrium flow physics in the transition and rarefied
flow regimes. As a result, the current method can be useful in the flow simulation
where both continuum and rarefied flow physics needs to be resolved in a single computation. This paper will extensively evaluate the performance of the unified scheme
from free molecule to continuum NS solutions, and from low speed micro-flow to high
speed non-equilibrium aerodynamics. The test cases clearly demonstrate that the unified scheme is a reliable method for the rarefied flow computations, and the scheme
provides an important tool in the study of non-equilibrium flow.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.030511.220911a},
url = {http://global-sci.org/intro/article_detail/cicp/7308.html}
}