Computing nearly singular solutions using pseudo-spectral methods

doi:10.1016/j.jcp.2007.04.014

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	Computing nearly singular solutions using pseudo-spectral methods
	Hou, Thomas Y.; Li, Ruo
	2007-09-10
发表期刊	JOURNAL OF COMPUTATIONAL PHYSICS
ISSN	0021-9991
卷号	226 期号:1 页码:379-397
摘要	In this paper, we investigate the performance of pseudo-spectral methods in computing nearly singular solutions of fluid dynamics equations. We consider two different ways of removing the aliasing errors in a pseudo-spectral method. The first one is the traditional 2/3 dealiasing rule. The second one is a high (36th) order Fourier smoothing which keeps a significant portion of the Fourier modes beyond the 2/3 cut-off point in the Fourier spectrum for the 2/3 dealiasing method. Both the I D Burgers equation and the 3D incompressible Euler equations are considered. We demonstrate that the pseudo-spectral method with the high order Fourier smoothing gives a much better performance than the pseudo-spectral method with the 2/3 dealiasing rule. Moreover, we show that the high order Fourier smoothing method captures about 12-15% more effective Fourier modes in each dimension than the 2/3 dealiasing method. For the 3D Euler equations, the gain in the effective Fourier codes for the high order Fourier smoothing method can be as large as 20% over the 2/3 dealiasing method. Another interesting observation is that the error produced by the high order Fourier smoothing method is highly localized near the region where the solution is most singular, while the 2/3 dealiasing method tends to produce oscillations in the entire domain. The high order Fourier smoothing method is also found be very stable dynamically. No high frequency instability has been observed. In the case of the 3D Euler equations, the energy is conserved up to at least six digits of accuracy throughout the computations. (C) 2007 Elsevier Inc. All rights reserved.
关键词	pseudo spectral methods singular solutions incompressible flow dealiasing
DOI	10.1016/j.jcp.2007.04.014
语种	英语
WOS研究方向	Computer Science ; Physics
WOS类目	Computer Science, Interdisciplinary Applications ; Physics, Mathematical
WOS记录号	WOS:000249936500017
出版者	ACADEMIC PRESS INC ELSEVIER SCIENCE
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/4319
专题	中国科学院数学与系统科学研究院
通讯作者	Hou, Thomas Y.
作者单位	1.CALTECH, Pasadena, CA 91125 USA 2.Chinese Acad Sci, LSEC, Acad Math & Syst Sci, Beijing 100080, Peoples R China 3.Peking Univ, LMAM, Beijing 100871, Peoples R China 4.Peking Univ, Sch Math Sci, Beijing 100871, Peoples R China
推荐引用方式 GB/T 7714	Hou, Thomas Y.,Li, Ruo. Computing nearly singular solutions using pseudo-spectral methods[J]. JOURNAL OF COMPUTATIONAL PHYSICS,2007,226(1):379-397.
APA	Hou, Thomas Y.,&Li, Ruo.(2007).Computing nearly singular solutions using pseudo-spectral methods.JOURNAL OF COMPUTATIONAL PHYSICS,226(1),379-397.
MLA	Hou, Thomas Y.,et al."Computing nearly singular solutions using pseudo-spectral methods".JOURNAL OF COMPUTATIONAL PHYSICS 226.1(2007):379-397.