@Article{JCM-21-101, author = {}, 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 = {

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' equation and the compressible Navier-Stokes equations. We demonstrate that, for the second order scheme, $Rc\leq3$ is an appropriate constraint for numerical resolution of the viscous profile, while for the fourth-order schemes the constraint can be relaxed to $Rc\leq6$. Our study indicates that the fourth order scheme is preferable: better accuracy, higher resolution, and larger cell-Reynolds numbers.

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/10286.html} }