A second-order numerical method for elliptic equations with singular sources using local flter |
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Authors: | Jiang Yongsong Fang Le Jing Xiaodong Sun Xiaofeng Francis Leboeuf |
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Institution: | 1. Department of Compressor Design, AVIC Shenyang Engine Design and Research Institute, Shenyang 110015, China;2. School of Energy and Power Engineering, Beihang University, Beijing 100191, China;3. Ecole Centrale de Pékin, Laboratoire International Associé, Beihang University, Beijing 100191, China;4. MOE Key Laboratory of High-speed Railway Engineering, Southwest Jiaotong University, Chengdu 610031, China;5. Ecole Centrale de Lyon, Laboratoire de Mécanique des Fluides et d’Acoustique, Université de Lyon, Ecully 69134, France |
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Abstract: | 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. |
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Keywords: | Computational aerodynamics Immersed boundary method Immersed interface method Kernel flter Singular source |
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