多项式基函数法

吴望一; 林光

doi:10.3879/j.issn.1000-0887.2009.09.003

多项式基函数法

doi: 10.3879/j.issn.1000-0887.2009.09.003

吴望一,
林光

北京大学工学院湍流与复杂系统国家重点实验室, 力学与空天技术系, 北京 100871

基金项目: 国家自然科学(重点)基金资助项目(19889210)

详细信息

作者简介:
吴望一(1933- ),男,浙江镇海人,教授(联系人.E-mail:wuwy@pku.edu.cn).

中图分类号: V211.3
计量
- 文章访问数: 1664
- HTML全文浏览量: 70
- PDF下载量: 887
- 被引次数: 0
出版历程
- 收稿日期: 2009-04-14
- 修回日期: 2009-07-30
- 刊出日期: 2009-09-15

Basic Function Scheme of Polynomial Type

State Key Laboratory for Turbulence and Complex System, Department of Mechanics and Aerospace Engineering, College of Engineering, Peking University, Beijing 100871, P. R. China

摘要

摘要: 提出一种新型的数值计算方法——基函数法．此方法直接在非结构网格上离散微分算子．采用基函数展开逼近真实函数，构造出了导数的中心格式和迎风格式．取二阶多项式为基函数，并采用通量分裂法及中心格式和迎风格式相结合的技术以消除激波附近的非物理波动，构造出数值求解无粘可压缩流动二阶多项式的基函数格式．通过多个二维无粘超音速和跨音速可压缩流动典型算例的数值计算表明，该方法是一种高精度的、对激波具有高分辨率的无波动新型数值计算方法，与网格自适应技术相结合可得到十分满意的结果．
- 多项式基函数法 /
- 新型数值计算方法 /
- 非结构网格
Abstract: A new numerical method-Basic Function Method was proposed.This method could directly discrete differential operator on unstructured grids.By using the expansion of basic function to approach the exact function,the central and upwind schemes of derivative were constructed.By using the second-order polynomial as basic function and applying the technique of flux splitting method and the combination of central and upwind schemes to suppress the non-physical fluctuation near the shock wave,the second-order basic function scheme of polynomial type for solving inviscid compressible flow numerically was constructed.Several numerical results of many typical examples for two dimensional inviscid compressible transonic and supersonic steady flow illustrate that it is a new scheme with high accuracy and high resolution for shock wave.Especially,combined with the adaptive remeshing technique,the satisfactory results can be obtained by these schemes.
- basic function scheme of polynomial type /
- new numerical method /
- unstructured grid

HTML全文

参考文献(8)

[1]	张涵信.无波动、无自由参数的耗散差分格式[J].空气动力学学报,1988,6（2）:143-165.
[2]	吴望一,蔡庆东.非结构网格上一种新型的高分辨率高精度无波动的有限元格式[J].中国科学（A辑）,1998,28（7）:633-643 .
[3]	Peraire J,Vahdati M,Morgan K,et al.Adaptive remeshing for compressible flow computations[J].Journal of Computational Physics,1987,72(2):449-466. doi: 10.1016/0021-9991(87)90093-3
[4]	谢文俊.基函数法在三维无粘可压缩流动中的研究与应用以及三维非结构网格的生成及自适应技术研究[D].硕士研究生学位论文.北京：北京大学，2002.
[5]	Zeeuw D D,Powell K G.An adaptively refined cartesian mesh solver for the Euler equations[J].Journal of Computational Physics,1993,104(1):56-68. doi: 10.1006/jcph.1993.1007
[6]	Yee H C,Harten A.Implicit TVD scheme for hyperbolic conservation laws in curvilinear coordinates[J].AIAAJ,1987,25(2):266-274. doi: 10.2514/3.9617
[7]	Hwang C J, Wu S J. Adaptive finite upwind approach on mixed quadrilateral-triangular meshes[J]. AIAAJ,1993,31(1):61-67. doi: 10.2514/3.11319
[8]	Lyubimov A N,Rusanov V V.Gas flow past blunt bodies[R]. NASA-TT-F715,1973.