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直角坐标网格下LSFD方法的显式公式和性能研究

蔡庆东

蔡庆东. 直角坐标网格下LSFD方法的显式公式和性能研究[J]. 应用数学和力学, 2009, 30(2): 179-191.
引用本文: 蔡庆东. 直角坐标网格下LSFD方法的显式公式和性能研究[J]. 应用数学和力学, 2009, 30(2): 179-191.
CAI Qing-dong. Explicit Formulations and Performance Study of LSFD Method on Cartesian Mesh[J]. Applied Mathematics and Mechanics, 2009, 30(2): 179-191.
Citation: CAI Qing-dong. Explicit Formulations and Performance Study of LSFD Method on Cartesian Mesh[J]. Applied Mathematics and Mechanics, 2009, 30(2): 179-191.

直角坐标网格下LSFD方法的显式公式和性能研究

基金项目: 国家自然科学基金资助项目(10872005;10532010)
详细信息
    作者简介:

    蔡庆东(1968- ),男,吉林松原人,副教授,博士(Tel:+86-10-62757942;E-mail:caiqd@pku.edu.cn).

  • 中图分类号: O241.82;O242

Explicit Formulations and Performance Study of LSFD Method on Cartesian Mesh

  • 摘要: 重点讨论了LSFD(least square-based finite difference)方法和传统的FD(finite difference)方法在性能上的对比问题.对于传统的中心差分格式,一阶导数和二阶导数在二维情况的数值格式基架点有9个点,三维情况有27个点.在同样的基架点下,给出了LSFD方法近似一阶导数和二阶导数的显式公式,并指出LSFD方法在这种情况下实质上就是在不同网格线上的传统中心差分格式的组合. 在数值模拟中,LSFD方法达到收敛所需要的迭代步数比传统差分格式少,并且x和y方向的网格纵横尺度比在LSFD方法中是一个非常重要的参数,对计算的稳定性有重要影响.
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出版历程
  • 收稿日期:  2008-06-05
  • 修回日期:  2008-10-20
  • 刊出日期:  2009-02-15

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