@Article{CiCP-28-539,
author = {Ji , Xing and Xu , Kun},
title = {Performance Enhancement for High-Order Gas-Kinetic Scheme Based on WENO-Adaptive-Order Reconstruction},
journal = {Communications in Computational Physics},
year = {2020},
volume = {28},
number = {2},
pages = {539--590},
abstract = {<p style="text-align: justify;">High-order gas-kinetic scheme (HGKS) has been well-developed in the past
years. Abundant numerical tests including hypersonic flow, turbulence, and aeroacoustic problems, have been used to validate its accuracy, efficiency, and robustness.
However, there is still room for its further improvement. Firstly, the reconstruction
in the previous scheme mainly achieves a fifth-order accuracy for the point-wise values at a cell interface due to the use of standard WENO reconstruction, and the slopes
of the initial non-equilibrium states have to be reconstructed from the cell interface
values and cell averages again. The same order of accuracy for slopes as the original
WENO scheme cannot be achieved. At the same time, the equilibrium state in space
and time in HGKS has to be reconstructed separately. Secondly, it is complicated to get
reconstructed data at Gaussian points from the WENO-type method in high dimensions. For HGKS, besides the point-wise values at the Gaussian points it also requires
the slopes in both normal and tangential directions of a cell interface. Thirdly, there exists visible spurious overshoot/undershoot at weak discontinuities from the previous
HGKS with the standard WENO reconstruction. In order to overcome these difficulties, in this paper we use an improved reconstruction for HGKS. The WENO with
adaptive order (WENO-AO) [2] method is implemented for reconstruction. Equipped
with WENO-AO reconstruction, the performance enhancement of HGKS is fully explored. WENO-AO not only provides the interface values, but also the slopes. In other
words, a whole polynomial inside each cell is provided by the WENO-AO reconstruction. The available polynomial may not benefit to the high-order schemes based on the
Riemann solver, where only points-wise values at the cell interface are needed. But,
it can be fully utilized in the HGKS. As a result, the HGKS becomes simpler than the
previous one with the direct implementation of cell interface values and their slopes
from WENO-AO. The additional reconstruction of equilibrium state at the beginning
of each time step can be avoided as well by dynamically merging the reconstructed non-equilibrium slopes. The new HGKS essentially releases or totally removes the
above existing problems in the previous HGKS. The accuracy of the scheme from 1D
to 3D from the new HGKS can recover the theoretical order of accuracy of the WENO
reconstruction. In the two- and three-dimensional simulations, the new HGKS shows
better robustness and efficiency than the previous scheme in all test cases.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.OA-2019-0082},
url = {http://global-sci.org/intro/article_detail/cicp/16941.html}
}