TY - JOUR
T1 - High-Order Unified Gas-Kinetic Scheme
AU - Lim , Gyuha
AU - Zhu , Yajun
AU - Xu , Kun
JO - Communications in Computational Physics
VL - 4
SP - 951
EP - 979
PY - 2022
DA - 2022/10
SN - 32
DO - http://doi.org/10.4208/cicp.OA-2022-0113
UR - https://global-sci.org/intro/article_detail/cicp/21135.html
KW - High-order reconstruction, two-stage fourth-order scheme, WENO-AO, micro flow.
AB - <p style="text-align: justify;">In this paper, we present a high-order unified gas-kinetic scheme (UGKS)
using the weighted essentially non-oscillatory with adaptive-order (WENO-AO)
method for spatial reconstruction and the two-stage fourth-order scheme for time evolution. Since the UGKS updates both the macroscopic flow variables and microscopic
distribution function, and provides an adaptive flux function by combining the equilibrium and non-equilibrium parts, it is possible to take separate treatment of the equilibrium and non-equilibrium calculation in the UGKS for the development of high-order scheme. Considering the fact that high-order techniques are commonly applied
in the continuum flow simulation with complex structures, and that the rarefied flow
structure is usually smooth in the physical space, we apply the high-order techniques
in the equilibrium part of the UGKS for the capturing of macroscopic flow evolution,
and retain the calculation of distribution function as a second-order method, so that
a balance of computational cost and numerical accuracy could be well achieved. The
HUGKS has been validated by several numerical test cases, including sine-wave accuracy test, Sod-shock tube, Couette, oscillating Couette, lid-driven cavity and oscillating
cavity flow. It is shown that the current method preserves the multiscale property of
the original UGKS and obtains accurate solutions in the near continuum regimes.</p>