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高精度隐式参差光滑格式的构造

倪明玖 席光 王尚锦

倪明玖, 席光, 王尚锦. 高精度隐式参差光滑格式的构造[J]. 应用数学和力学, 2000, 21(4): 365-372.
引用本文: 倪明玖, 席光, 王尚锦. 高精度隐式参差光滑格式的构造[J]. 应用数学和力学, 2000, 21(4): 365-372.
Ni Migjiu, Xi Guang, Wang Shangjin. Construction of High-Order Accuracy Implicit Residual Smoothing Schemes[J]. Applied Mathematics and Mechanics, 2000, 21(4): 365-372.
Citation: Ni Migjiu, Xi Guang, Wang Shangjin. Construction of High-Order Accuracy Implicit Residual Smoothing Schemes[J]. Applied Mathematics and Mechanics, 2000, 21(4): 365-372.

高精度隐式参差光滑格式的构造

基金项目: 国家教委博士点资金
详细信息
  • 中图分类号: O363

Construction of High-Order Accuracy Implicit Residual Smoothing Schemes

  • 摘要: 参照Lax-Wendroff格式的构造方法,就双曲型方程、抛物型方程和双曲-抛物型方程,构造了一种新的IRS(implicit residual smoothing)格式。该IRS格式有二阶或三阶时间精度且大大地拓宽了解的稳定区域和CFL数。这种新的IRS格式有中心加权型和迎风偏向型两种,并用von-Neumann分析方法分析了格式的稳定范围。讨论了在透平机械中广泛应用的Dawes方法的局限性,发现该方法对稳态问题得出的解与时间步长的选取有关,对粘性问题求解时,时间步长受严格限制。最后,结合TVD(total variation diminishing)格式和四阶Runge-Kutta技术,用IRS格式和Dawes方法对二维反射激波场进行了数值模拟,数值结果支持本文的分析结论。
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出版历程
  • 收稿日期:  1998-01-06
  • 修回日期:  1999-12-03
  • 刊出日期:  2000-04-15

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