时间空间均为二阶的新型NND差分格式

吴望一; 蔡庆东

时间空间均为二阶的新型NND差分格式

吴望一¹,
蔡庆东²

1.
北京大学力学与工程科学系, 北京 100871;
2.
北京大学湍流研究国家重点实验室, 北京 100871

详细信息

作者简介:
吴望一(1933~ ),男,浙江镇海人,教授,博导,发表论文82篇;蔡庆东(1968~ ),男,吉林松沅人,副教授.

中图分类号: O354.5;O241.3
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- 文章访问数: 2893
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- 被引次数: 0
出版历程
- 收稿日期: 1999-04-06
- 修回日期: 1999-12-08
- 刊出日期: 2000-06-15

A New NND Difference Scheme of Second Order in Time and Space

Wu Wangyi¹,
Cai Qingdong²

1.
Department of Mechanics and Engineering Science, Peking University, Beijing 100871, P R China;
2.
State Key Laboratory for Turbulence Research, Peking University, Beijing 100871, P R China

摘要

摘要: 张涵信的研究表明,为了避免激波前后差分解的波动,在差分格式的改型方程中三阶导数的系数在激波上游必须是正的,而在激波下游则必须是负的.据此提出了一种新型的无波动、无自由参数耗散性的差分格式,它对时间和空间都是二阶的.证明了此格式是TVD的,而且是推广的二阶Годунов格式.在处理有激波的流场时,此格式是Lax-Wendroff格式的改进和推广.给出了若干算例,计算结果表明,此格式不仅无波动,而且具有形式紧凑、应用方便、分辨率高、稳定性准则中的Courant数较大的优点.
- 新型NND差分格式 /
- 欧拉方程
Abstract: The study by Zhang Hanxin shows that in order to suppress the spurious oscillation at both upstream and downstream of the shock,the coefficient of the third order derivative on the right hand side of the modified equation of the difference scheme must be positive upstream and negative downstream of the shock.According to this principle,a new non-oscillatory,containing no free parameters and dissipative difference scheme of second order both in time and space is proposed.It is proved that this scheme possesses TVD property and is generalized Gudunov scheme of second order.In the presence of the shock wave in the flow field,this scheme is the generalization and improvement of the Lax-Wendroff scheme'several numerical examples are given which demonstrate that the proposed scheme is nonoscillatory of high order accuracy and high resolution.It also has the advantages of compact form,greater maximum allowable Courant number and convenient to use.
- new NND difference scheme /
- Euler equation

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参考文献(5)

[1]	张涵信.差分计算中激波上、下解出现波动的探讨[J].空气动力学学报,1984,2(1):12~19.
[2]	张涵信.无波动,无自然参数的耗散差分格式[J].空气动力学学报,1988,6(2):143~165.
[3]	Anderson A,Tannehill C,Pletcher H.Computational Fluid Mechan ics and Heat Tr ansfer[M].McGraw-Hill Book Company,1984.
[4]	Warming R P,Hyett B J.The modified equation approach to the stability and accuracy analysis of finite-difference methods[J].J Com put Phys,1974,14:159~179.
[5]	吴望一.新型无波动、无自由参数的二阶TVD差分格式[A].见:全国第五届计算流体力学会议论文集[C].太平,1990.