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论文:2013,Vol:31,Issue(1):94-97 |
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郭永恒, 杨永, 刘逸鸥, 张强. 一种新型的节点间断Galerkin格式滤波器设计[J]. 西北工业大学 |
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Guo Yongheng, Yang Yong, Liu Yiou, Zhang Qiang. An Original Designed Filter for Nodal Discontinuous Galerkin Method[J]. Northwestern polytechnical university |
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| 一种新型的节点间断Galerkin格式滤波器设计 |
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| 郭永恒, 杨永, 刘逸鸥, 张强 |
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| 西北工业大学 翼型叶栅空气动力学国防科技重点实验室, 陕西 西安 710072 |
| 摘要: |
| 使用高阶数值格式求解双曲守恒律时,在间断解附近产生的Gibbs振荡很容易导致非物理解的产生,从而使计算过程中断。文章以节点间断Galerkin格式为背景,使用广义Fourier级数这一分析工具,提出了相对振荡强度的概念,并以此作为滤波器的筛查对象;构造了新的指数型罚函数,它能够根据振荡的强弱,自动识别非物理解的广义Fourier分量并加以过滤。在这项算法的支持下,利用节点间断Galerkin格式顺利求解了Euler方程,数值模拟了超临界翼型RAE2822翼型的跨声速外流场和超燃冲压发动机的超声速内流场。结果表明,在这种新型的滤波器基础上,不仅很好地捕捉到了激波的正确位置,而且有效地抑制了激波附近的非物理振荡。 |
| 关键词:
节点间断Galerkin
相对振荡强度
广义Fourier级数
滤波器
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| An Original Designed Filter for Nodal Discontinuous Galerkin Method |
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| Guo Yongheng, Yang Yong, Liu Yiou, Zhang Qiang |
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| National Key Laboratory of Aerodynamic Design and Research,Northwestern Polytechnical University,Xi'an 710072,China |
| Abstract: |
| When the high-order numerical method for the hyperbolic conservation laws is applied, the correspond-ing Gibbs oscillations occurring near the discontinuous regions can easily generate nonphysical solutions, leading tothe termination of the calculating process.Based on the nodal discontinuous Galerkin methods, the generalizedFourier series are adopted, while a conception of relative oscillation strength is proposed, according to which the fil-ter is used.Additionally, an exponential penalty function is originally designed such that it can automatically distin-guish and filter out the generalized Fourier component of nonphysical solutions following the strength of oscillations.Supported by this method, the Euler equations are solved in the nodal discontinuous Galerkin form, and the tran-sonic external flow fields of RAE2822 airfoil as well as the supersonic internal flow fields of scramjet combustor arenumerically simulated accordingly.Simulation results and their analysis illustrate that, based on this original de-signed filter, the exact position of shock wave can be captured successfully, and the nonphysical oscillations nearthe shock can be efficiently damped. |
| Key words:
combustors
computer simulation
design
efficiency
Euler equations
flow fields;filter
generalizedFourier series
nodal discontinuous Galerkin method
relative oscillation strength
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| 收稿日期: 2012-04-28
修回日期:
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| DOI: |
| 基金项目: 国家自然科学基金(11002117)资助 |
| 通讯作者:
Email： |
| 作者简介: 郭永恒(1982-)，西北工业大学博士研究生，主要从事理论与计算流体力学的研究。
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| 作者相关文章 |
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| 郭永恒 在本刊中的所有文章 |
| 杨永 在本刊中的所有文章 |
| 刘逸鸥 在本刊中的所有文章 |
| 张强 在本刊中的所有文章 |
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参考文献: |
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[1] Jan S Hesthaven,Tim Warburton.Nodal Discontinuous Galerkin Methods: Algorithms,Analysis,and Applications.Springer,2008,135-145
[2] Peter Sturdza.A Quasi-Simultaneous Interactive Boundary-Layer Model for a Cartesian Solver.50th AIAA Aerospace SciencesMeeting Including the New Horizons Forum and Aerospace Exposition,2012,13-15
[3] Shuangzhang Tu,Shahrouz Aliabadi.A Slope Limiting Procedure in Discontinuous Galerkin Finite Element Method for Gasdy-namics Applications.International Journal of Numerical Analysis and Modeling,2005,2(2): 163-178 |
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