非结构三角形网格的一个ENO型有限体积方法

宋松和; 陈矛章

非结构三角形网格的一个ENO型有限体积方法

北京航空航天大学动力系

详细信息

中图分类号: O 24182
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出版历程
- 收稿日期: 1998-07-02
- 网络出版日期: 1998-06-30

ENO Finite Volume Method For Unstructured Triangular Mesh

Beijing University of Aeronautics and Astronautics,Dept. of Jet Propulsion

摘要

摘要: 基于双曲型守恒律方程,对非结构三角形网格给出了一种ENO(Essentially Nonoscillatory Scheme)型有限体积格式,方法的主要思想是先对每一个三角形单元构造一个加权的二次插值多项式,而在计算交界面的流通量时采用了两点高斯积分公式以保证格式的整体精度,时间离散采用三阶TVD Runge-Kutta方法.最后给出了该格式收敛的数值阶,并对前台阶问题进行了计算.
- 双曲型方程 /
- 高斯求积公式 /
- 龙格-库塔法 /
- 非结构网格 /
- 有限体积方法
Abstract: A third order ENO finite volume method for hyperbolic conservation laws on unstructured triangular mesh is introduced.In order to obtain the third order accuracy on spatial discretization,a weighted quadratic interpolation is constructed on every triangular mesh.Two point Gauss quadrature formula is also used on each edge of every triangular mesh and the third order TVD Runge-Kutta method is used for time discretization.The numerical order of convergence and the numerical result of a mesh 3 wind tunnel with one step are given.The numerical results show that the numerical order of new method approachs to 3.
- hyperbolic equations /
- quadrature formulas of Gauss /
- Runge-Kutta method /
- unstructrued mesh /
- finite volume method

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参考文献(1)

1. Harten A. High resolution schemes for hyperbolic conservation laws. J Comp Phy, 1983,49(3):357~393 2. Harten A, Osher S, Uniformly high order accurate nonoscillatory schemes I. SIAM J Num Anal, 1987,24(2):214~309 3. Harten A, Engquist B,Osher S, et al. Uniformly high order accurate essentially nonoscillatory schemes Ⅲ. J Comp Phy, 1987,71(1):231~303 4. Shu C W, Osher S. Effient implementation of essentially nonoscillatory shock capturing schemes. J Comp Phy, 1988,77(2):439~471 5. Shu C W, Osher S. Effient implementation of essentially nonoscillatory shock capturing schemes Ⅱ. J Comp Phy,1989,83(1):32~78 6. Liu X D, Osher S, Chan T. Weighted essentially nonoscillatory schemes. J Comp Phy, 1994,115(2):200~212 7. Jiang G S, Shu C W. Efficient implementation of weighted ENO schemes. J Comp Phy, 1996,126(2):202~228 8. Abgrall R. On essentially non-oscillatory schemes on unstructured meshes:analysis and implementation. J Comp Phy, 1994,114(1):45~58 9. Durlofsky L J, Engquist B, Osher S. Triangle based adaptive stencil for the solution of hyperbolic conservation laws. J Comp Phy, 1992,98(1):64~73 10. Liu X D. A maximum principle satisfying modification of triangle based adaptive stencils for the solution of scalar hyperbolic conservation laws. SIAM J Numer Anal, 1993,30(3):701~716 11. Song S H, Li Y F. A class of finite volume scheme satisfying maximum principle for 2d scalar hyperbolic conservation laws on unstructured triangular meshes. Chinese J Num Math & Appl,1997,19(4):30~38 12. 宋松和. 非结构网格有限体积方法的研究:[学位论文].北京:中国科学院计算数学与科学工程计算研究所,1996

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