@Article{JCM-21-101,
author = {Weizhu Bao and Shi Jin},
title = {High-Order I-Stable Centered Difference Schemes for Viscous Compressible Flows},
journal = {Journal of Computational Mathematics},
year = {2003},
volume = {21},
number = {1},
pages = {101--112},
abstract = {<p style="text-align: justify;">In this paper we present high-order I-stable centered difference schemes for the numerical simulation of viscous compressible flows. Here I-stability refers to time discretizations whose linear stability regions contain part of the imaginary axis. This class of schemes has a numerical stability independent of the cell-Reynolds number $Rc$, thus allows one to simulate high Reynolds number flows with relatively larger $Rc$, or coarser grids for a fixed $Rc$. On the other hand, $Rc$ cannot be arbitrarily large if one tries to obtain adequate numerical resolution of the viscous behavior. We investigate the behavior of high-order I-stable schemes for Burgers&#39; equation and the compressible Navier-Stokes equations. We demonstrate that, for the second order scheme,&nbsp;<span style="text-align: justify;">$Rc\leq3$ is an appropriate constraint for numerical resolution of the viscous profile, while for the fourth-order schemes the constraint can be relaxed to</span>&nbsp;$Rc\leq6$. Our study indicates that the fourth order scheme is preferable: better accuracy, higher resolution, and larger cell-Reynolds numbers.</p>},
issn = {1991-7139},
doi = {https://doi.org/},
url = {http://global-sci.org/intro/article_detail/jcm/10286.html}
}