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A second-order numerical method for elliptic equations with singular sources using local filter
Alternative TitleA second-order numerical method for elliptic equations with singular sources using local filter
Jiang Yongsong1; Fang Le2; Jing Xiaodong2; Sun Xiaofeng2; Francis Leboeuf4
2013
Source PublicationCHINESE JOURNAL OF AERONAUTICS
ISSN1000-9361
Volume26Issue:6Pages:1398-1408
AbstractThe presence of Dirac delta function in differential equation can lead to a discontinuity, which may degrade the accuracy of related numerical methods. To improve the accuracy, a second-order numerical method for elliptic equations with singular sources is introduced by employing a local kernel filter. In this method, the discontinuous equation is convoluted with the kernel function to obtain a more regular one. Then the original equation is replaced by this filtered equation around the singular points, to obtain discrete numerical form. The unchanged equations at the other points are discretized by using a central difference scheme. 1D and 2D examples are carried out to validate the correctness and accuracy of the present method. The results show that a second-order of accuracy can be obtained in the filtering framework with an appropriate integration rule. Furthermore, the present method does not need any jump condition, and also has extremely simple form that can be easily extended to high dimensional cases and complex geometry. (C) 2013 Production and hosting by Elsevier Ltd. on behalf of CSAA & BUAA.
Other AbstractThe presence of Dirac delta function in differential equation can lead to a discontinuity, which may degrade the accuracy of related numerical methods. To improve the accuracy, a second-order numerical method for elliptic equations with singular sources is introduced by employing a local kernel filter. In this method, the discontinuous equation is convoluted with the kernel function to obtain a more regular one. Then the original equation is replaced by this filtered equation around the singular points, to obtain discrete numerical form. The unchanged equations at the other points are discretized by using a central difference scheme. 1D and 2D examples are carried out to validate the correctness and accuracy of the present method. The results show that a second-order of accu-racy can be obtained in the filtering framework with an appropriate integration rule. Furthermore, the present method does not need any jump condition, and also has extremely simple form that can be easily extended to high dimensional cases and complex geometry.
KeywordIMMERSED INTERFACE METHOD SMOOTHED PARTICLE HYDRODYNAMICS BOUNDARY METHOD DISCONTINUOUS COEFFICIENTS GLOBAL DESCRIPTION FLOW ORDER SIMULATION ACCURACY Computational aerodynamics Immersed boundary method Immersed interface method Kernel filter Singular source
Indexed ByCSCD
Language英语
Funding Project[National Natural Science Foundation in China] ; [BUAA SJP "111'' Program] ; [National Basic Research Program of China] ; [Open Research Fund of MOE Key Laboratory of High-speed Railway Engineering, Southwest Jiaotong University] ; [European Community's Seventh Framework Program]
CSCD IDCSCD:5027626
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Document Type期刊论文
Identifierhttp://ir.imr.ac.cn/handle/321006/147665
Collection中国科学院金属研究所
Affiliation1.中国科学院金属研究所
2.北京航空航天大学
3.西南交通大学
4.University Lyon, Ecole Cent Lyon, Lab Mecan Fluides & Acoust, F-69134 Ecully, France
Recommended Citation
GB/T 7714
Jiang Yongsong,Fang Le,Jing Xiaodong,et al. A second-order numerical method for elliptic equations with singular sources using local filter[J]. CHINESE JOURNAL OF AERONAUTICS,2013,26(6):1398-1408.
APA Jiang Yongsong,Fang Le,Jing Xiaodong,Sun Xiaofeng,&Francis Leboeuf.(2013).A second-order numerical method for elliptic equations with singular sources using local filter.CHINESE JOURNAL OF AERONAUTICS,26(6),1398-1408.
MLA Jiang Yongsong,et al."A second-order numerical method for elliptic equations with singular sources using local filter".CHINESE JOURNAL OF AERONAUTICS 26.6(2013):1398-1408.
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