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Applied Mathematics and Mechanics (English Edition) ›› 2009, Vol. 30 ›› Issue (9): 1091-1103.doi: https://doi.org/10.1007/s10483-009-0903-y

• Articles • 上一篇    下一篇

Basic function scheme of polynomial type

吴望一 林光   

  1. State Key Laboratory for Turbulence and Complex System, Department of Mechanics and Aerospace Engineering, College of Engineering, Peking University,Beijing 100871, P. R. China
  • 收稿日期:2009-04-14 修回日期:2009-07-30 出版日期:2009-09-01 发布日期:2009-09-01

Basic function scheme of polynomial type

WU Wang-Yi, LIN Guang   

  1. State Key Laboratory for Turbulence and Complex System, Department of Mechanics and Aerospace Engineering, College of Engineering, Peking University,Beijing 100871, P. R. China
  • Received:2009-04-14 Revised:2009-07-30 Online:2009-09-01 Published:2009-09-01

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摘要： A new numerical method named as basic function method is proposed. It can directly discretize differential operators on unstructured grids. By expanding the basic function to approach the exact function, the central and upwind schemes of derivative are constructed. By using the second-order polynomial as a basic function and applying the flux splitting method and the combination of central and upwind schemes to suppress non-physical fluctuation near shock waves, a second-order basic function scheme of polynomial type is proposed to solve inviscid compressible flows numerically. Numerical results of typical examples for two-dimensional inviscid compressible transonic and supersonic steady flows indicate that the new scheme has high accuracy and high resolution for shock waves. Combined with the adaptive remeshing technique, satisfactory results can be obtained.

关键词: basic function scheme of polynomial type, new numerical method, unstructured grids

Abstract: A new numerical method named as basic function method is proposed. It can directly discretize differential operators on unstructured grids. By expanding the basic function to approach the exact function, the central and upwind schemes of derivative are constructed. By using the second-order polynomial as a basic function and applying the flux splitting method and the combination of central and upwind schemes to suppress non-physical fluctuation near shock waves, a second-order basic function scheme of polynomial type is proposed to solve inviscid compressible flows numerically. Numerical results of typical examples for two-dimensional inviscid compressible transonic and supersonic steady flows indicate that the new scheme has high accuracy and high resolution for shock waves. Combined with the adaptive remeshing technique, satisfactory results can be obtained.

Key words: basic function scheme of polynomial type, new numerical method, unstructured grids

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