HIGH-ORDER I-STABLE CENTERED DIFFERENCE SCHEMES FOR VISCOUS COMPRESSIBLE FLOWS

• 来源期刊: 计算数学（英文版）
• 学科: 数学
• 关键词: I-stable Viscous compressible flow Burgers' equation Cell-Reynolds number constraint.
• 年，卷（期）: 2003,（1）
• 页码范围: 101-112
• 页数: 12页
• 分类号: O1
• 语种: 英文

摘要

In this paper we present high-order I-stable centered difference schemes for the numer-ical simulation of viscous compressible flows. Here I-stability refers to time discretizationswhose linear stability regions contain part of the imaginary axis. This class of schemeshas a numerical stability independent of the cell-Reynolds number Rc, thus allows one tosimulate high Reynolds number flows with relatively larger Rc, or coarser grids for a fixedRc. On the other hand, Rc cannot be arbitrarily large if one tries to obtain adequatenumerical resolution of the viscous behavior. We investigate the behavior of high-orderI-stable schemes for Burgers' equation and the compressible Navier-Stokes equations. Wedemonstrate that, for the second order scheme, Rc ≤ 3 is an appropriate constraint for nu-merical resolution of the viscous profile, while for the fourth-order schemes the constraintcan be relaxed to Rc ≤ 6. Our study indicates that the fourth order scheme is preferable:better accuracy, higher resolution, and larger cell-Reynolds numbers.