Interpolation functions in the immersed boundary and finite element methods |
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Authors: | Xingshi Wang Lucy T Zhang |
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Affiliation: | 1. JEC 2049, Department of Mechanical, Aerospace, and Nuclear Engineering, Rensselaer Polytechnic Institute, Troy, NY, 12180, USA
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Abstract: | In this paper, we review the existing interpolation functions and introduce a finite element interpolation function to be
used in the immersed boundary and finite element methods. This straightforward finite element interpolation function for unstructured
grids enables us to obtain a sharper interface that yields more accurate interfacial solutions. The solution accuracy is compared
with the existing interpolation functions such as the discretized Dirac delta function and the reproducing kernel interpolation
function. The finite element shape function is easy to implement and it naturally satisfies the reproducing condition. They
are interpolated through only one element layer instead of smearing to several elements. A pressure jump is clearly captured
at the fluid–solid interface. Two example problems are studied and results are compared with other numerical methods. A convergence
test is thoroughly conducted for the independent fluid and solid meshes in a fluid–structure interaction system. The required
mesh size ratio between the fluid and solid domains is obtained. |
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Keywords: | |
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