用于气动声学计算的非均匀网格紧致差分格式

陈志夫; 文桂林; 王艳广; 王明

用于气动声学计算的非均匀网格紧致差分格式

陈志夫^1,2, ,,
文桂林^1,2,
王艳广^1,2,
王明^1,2

1.
湖南大学汽车车身先进设计制造国家重点实验室,长沙 41008
2.
湖南大学航天技术研究所,长沙 410082

基金项目: 教育部长江学者与创新团队发展计划(531105050037); 湖南大学汽车车身先进设计制造国家重点实验室自主课题(61075003)

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出版历程
- 收稿日期: 2011-12-27
- 刊出日期: 2013-01-28

Compact finite difference schemes on non-uniform meshes for computational aeroacoustics

CHEN Zhi-fu^{1,2
, ,},
WEN Gui-lin^1,2,
WANG Yan-guang^1,2,
WANG Ming^1,2

1.
State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, Hunan University,Changsha 41008
2.
Institute of Space Technology,Hunan University,Changsha 410082,China

摘要

摘要: 为克服传统紧致差分格式在数值求解非均匀网格问题时产生的寄生波,构造了一种新的高精度紧致差分格式.通过泰勒展开分析方法,详细给出了格式系数的通用形式;利用傅里叶分析方法,分析了数值耗散、色散误差.以3对角6阶精度紧致差分格式求解均匀扰动网格问题为例,计算表明:色散值和耗散值随扰动因子的增加而更加趋近于精确值;当扰动因子大于0.213时,格式不稳定,当扰动因子小于等于0.213时,格式渐近稳定;对一维对流波和二维波传播的模拟计算所得数值解与精确解吻合,体现了该格式在求解非均匀网格问题时的优越性.
- 非均匀网格 /
- 气动声学 /
- 紧致差分格式 /
- 寄生波 /
- 耗散 /
- 色散 /
- 渐近稳定
Abstract: When the classic compact finite difference scheme was applied to practical problems using non-uniform meshes,the spurious numerical oscillations would be excited.A high accuracy of compact scheme was developed for this problem.The general expressions of the scheme's coefficients were derived through Taylor expansion analysis;then the numerical dispersion and dissipation were analyzed by using Fourier analysis method.For the case that the sixth-order tridiagonal compact scheme was applied to non-uniform meshes,the results are shown:the dispersion and dissipation values are closer to the exact solution with the increase of disturbance factor;the scheme is asymptotically stable when the disturbance factor is less than or equal to 0.213,otherwise it is the opposite;the results of numerical solution for one-dimensional convective wave and two-dimensional wave propagation agree well with the theoretical solution,which shows advantages in the simulation of non-uniform meshes for computational aeroacoustis.
- non-uniform mesh /
- aeroacoustic /
- compact difference scheme /
- spurious numerical oscillation /
- dissipation /
- dispersion /
- asymptotical stability

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