Volume 21, Issue 1
High-order I-stable Centered Difference Schemes for Viscous Compressible Flows

Weizhu Bao & Shi Jin

J. Comp. Math., 21 (2003), pp. 101-112

Published online: 2003-02

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  • 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 iscous behavior. We investigate the behavior of high-order I-stable schemes for Burgers' equation and the compressible Navier-stokes equations. Wedemonstrate that, for the second order scheme, Rc$\leq$6. Our study indicates that the fourth order schemeis preferable: better accuracy, higher resolution, and larger cell-Reynolds numbers.

  • Keywords

I-stable Viscous compressible flow Burgers' equation Cell-Reynolds number constraint

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@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 iscous behavior. We investigate the behavior of high-order I-stable schemes for Burgers' equation and the compressible Navier-stokes equations. Wedemonstrate that, for the second order scheme, Rc$\leq$6. Our study indicates that the fourth order schemeis preferable: better accuracy, higher resolution, and larger cell-Reynolds numbers. }, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/10286.html} }
TY - JOUR T1 - High-order I-stable Centered Difference Schemes for Viscous Compressible Flows JO - Journal of Computational Mathematics VL - 1 SP - 101 EP - 112 PY - 2003 DA - 2003/02 SN - 21 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/10286.html KW - I-stable KW - Viscous compressible flow KW - Burgers' equation KW - Cell-Reynolds number constraint AB - In this paper we present high-order I-stable centered difference schemes for the numerical simulation of viscous compressible flows. Here I-stability refers to time discretizations whose linear stability regions contain part of the imaginary axis. This class of schemes has a numerical stability independent of the cell-Reynolds number Rc, thus allows one to simulate high Reynolds number flows with relatively larger Rc, or coarser grids for a fixed Rc. on the other hand, Rc cannot be arbitrarily large if one tries to obtain adequate numerical resolution of the iscous behavior. We investigate the behavior of high-order I-stable schemes for Burgers' equation and the compressible Navier-stokes equations. Wedemonstrate that, for the second order scheme, Rc$\leq$6. Our study indicates that the fourth order schemeis preferable: better accuracy, higher resolution, and larger cell-Reynolds numbers.
Weizhu Bao & Shi Jin. (1970). High-order I-stable Centered Difference Schemes for Viscous Compressible Flows. Journal of Computational Mathematics. 21 (1). 101-112. doi:
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