Effect of the Regularized Delta Function on the Accuracy of the Immersed Boundary Method

GONG Zhao-xin; LU Chuan-jing; HUANG Hua-xiong

doi:10.3879/j.issn.1000-0887.2012.11.010

Volume 33 Issue 11

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GONG Zhao-xin, LU Chuan-jing, HUANG Hua-xiong. Effect of the Regularized Delta Function on the Accuracy of the Immersed Boundary Method[J]. Applied Mathematics and Mechanics, 2012, 33(11): 1352-1365. doi: 10.3879/j.issn.1000-0887.2012.11.010

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Effect of the Regularized Delta Function on the Accuracy of the Immersed Boundary Method

doi: 10.3879/j.issn.1000-0887.2012.11.010

¹Department of Mechanics, Shanghai Jiaotong University, Shanghai 200240, P.R.China;²MOE Key Laboratory of Hydrodynamics, Shanghai 200240, P.R.China;³Department of Mathematics and Statistics, York University, Toronto,Ontario, Canada M3J 1P3

Received Date: 2011-09-13
Rev Recd Date: 2012-07-17
Publish Date: 2012-11-15

Abstract

Abstract

The immersed boundary method was an effective technique for modeling and simulating fluid-structure interactions especially in the area of biomechanics. The effect of the regularized delta function on its accuracy was an important subject in the property study. The method of manufactured solutions was taken as the research means. The computational code was firstly verified to be mistaken free by using smooth manufactured solutions. Then a jump in the manufactured solution for pressure was introduced to study the accuracy of the immersed boundary method. Four kinds of the regularized delta function were taken to test its effects on accuracy analysis. By analyzing the discretization errors, the accuracy of the immersed boundary method was proved to be first order. Meanwhile, the results showed that the regularized delta function could not improve the accuracy, but could change the discretization errors on the entire computational domain.

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References

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