A note on pressure accuracy in immersed boundary method for Stokes flow |
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| Authors: | Kuan-Yu Chen Ko-An Feng Yongsam Kim Ming-Chih Lai |
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| Affiliation: | 1. Department of Applied Mathematics, National Chiao Tung University, 1001, Ta Hsueh Road, Hsinchu 30010, Taiwan;2. National Center for Theoretical Sciences, National Tsing Hua University, No. 101, Sec. 2, Kuang Fu Road, Hsinchu 30043, Taiwan;3. Department of Mathematics, Chung-Ang University, Dongjak-Gu, Heukseok-Dong 221, Seoul 156756, South Korea;4. Center of Mathematical Modeling and Scientific Computing and Department of Applied Mathematics, National Chiao Tung University, 1001, Ta Hsueh Road, Hsinchu 30010, Taiwan |
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| Abstract: | In this short note, we provide a simplified one-dimensional analysis and two-dimensional numerical experiments to predict that the overall accuracy for the pressure or indicator function in immersed boundary calculations is first-order accurate in L1 norm, half-order accurate in L2 norm, but has O(1) error in L∞ norm. Despite the pressure has O(1) error near the interface, the velocity field still has the first-order convergence in immersed boundary calculations. |
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| Keywords: | Immersed boundary method Pressure accuracy Discrete delta function Stokes flow |
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