High-order I-stable Centered Difference Schemes for Viscous Compressible Flows
Weizhu Bao 1, Shi Jin 21 Department of Computational Science Computational Science, National University of Singapore, Singapore 117543
2 Department of Mathematical Science, Tsinghua University, Beijing 100084, China
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.
Key words: I-stable; Viscous compressible flow; Burgers' equation; Cell-Reynolds number constraint.