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

作者：Jiang Yongsong; Fang Le^*; Jing Xiaodong; Sun Xiaofeng; Francis Leboeuf

来源：Chinese Journal of Aeronautics, 2013, 26(6): 1398-1408.

DOI：10.1016/j.cja.2013.07.004

• Computational aerodynamics
• Immersed boundary method
• Immersed interface method
• Kernel filter
• Singular source

The 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.

• 出版日期2013-12
• 单位北京航空航天大学; 西南交通大学