Numerical simulation based on CE/SE method for airfoil flow with shock wave
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摘要: 在二维四边形结构网格下,针对时空守恒元和解元(CE/SE, space-time Conservation Element and Solution Element)方法捕捉激波需要双倍空间网格点的问题,重新对守恒元和解元进行了定义,计算点同时包含单元中心和网格节点,并推导得到了新的CE/SE方法的计算公式.以此为基础,结合非敏感克朗数(CNIS, Courant Number Insensitive Scheme)计算格式和当地时间步长方法,对激波翼型流场进行数值模拟,并与原方法及AGARD报告进行对比.结果表明,对原CE/SE方法的改进是有效的,可明显提高激波分辨能力,并且激波前后无明显的数值震荡发生,新方法适合应用于翼型流场中捕捉激波.Abstract: A new numerical scheme was developed to avoid using double spatial grids to capture shock wave through the original space-time conservation element and solution element (CE/SE) method on the 2-D structured quadrilateral meshes. The design of the new scheme was based on the redefinition of conservation element and solution element as well as one of solution points involving both cell centers and vertices. Numerical simulations for flows around airfoils involving shock wave were implemented using the new scheme in combination with Courant number insensitive scheme(CNIS) and local time-stepping method. The results computed from the modified scheme, comparing with that achieved by the original CE/SE method and an advisory group for aerospace research and development(AGARD) report, show a better resolution of the shock wave and that there is no obvious numerical oscillatory before and after the shock wave. The new scheme provides a more accurate and stable means for computing shock waves in flows over airfoils.
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Key words:
- CE/SE method /
- airfoils /
- shock waves /
- Euler equations /
- numerical simulation
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