A second-order numerical method for elliptic equations with singular sources using local flter

作     者：Jiang Yongsong Fang Le Jing Xiaodong Sun Xiaofeng Francis Leboeuf 

作者机构：Department of Compressor DesignAVIC Shenyang Engine Design and Research Institute School of Energy and Power Engineering Beihang University Ecole Centrale de Pe'kin Laboratoire International Associe'Beihang University MOE Key Laboratory of High-speed Railway Engineering Southwest Jiaotong University Ecole Centrale de Lyon Laboratoire de Me'canique des Fluides et d’Acoustique Universite' de LyonEcully 69134France 

出 版 物：《Chinese Journal of Aeronautics》 (中国航空学报（英文版）)

年 卷 期：2013年第26卷第6期

页      面：1398-1408页

核心收录：

学科分类：080704[工学-流体机械及工程] 07[理学] 080103[工学-流体力学] 08[工学] 0807[工学-动力工程及工程热物理] 070104[理学-应用数学] 0802[工学-机械工程] 0825[工学-航空宇航科学与技术] 0701[理学-数学] 0801[工学-力学（可授工学、理学学位）] 

基　　金：supported by the National Natural Science Foundation in China(Grant Nos.51076006,11202013) BUAA SJP ‘‘111’’ Program(Grant No.B08009) the National Basic Research Program of China(2012CB720200) the Open Research Fund of MOE Key Lab-oratory of High-speed Railway Engineering,Southwest Jiao-tong University and the European Community’s Seventh Framework Program(FP7/2007-2013)under Grant agreement 225967‘‘NextMuSE’’ 

主　　题：Computational aerodynamics Immersed boundary method Immersed interface method Kernel flter Singular source 

摘      要：The presence of Dirac delta function in differential equation can lead to a discontinuity,which may degrade the accuracy of related numerical *** improve the accuracy,a secondorder numerical method for elliptic equations with singular sources is introduced by employing a local kernel *** this method,the discontinuous equation is convoluted with the kernel function to obtain a more regular *** the original equation is replaced by this fltered equation around the singular points,to obtain discrete numerical *** 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 *** results show that a second-order of accuracy can be obtained in the fltering framework with an appropriate integration ***,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.