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A Divergence-Free Immersed Boundary Method and Its Finite Element Applications

Published online by Cambridge University Press:  06 August 2020

Chuan Zhou Open the ORCID record for Chuan Zhou [Opens in a new window] ,
Jianhua Li ,
Huaan Wang ,
Kailong Mu  and
Lanhao Zhao
Chuan Zhou*
Affiliation:
China Energy Engineering Group Guangdong Electric Power Design Institute Co., Ltd Guangzhou, China Guangdong Kenuo Surveying Engineering Co., Ltd Guangzhou, China
Jianhua Li
Affiliation:
China Energy Engineering Group Guangdong Electric Power Design Institute Co., Ltd Guangzhou, China Guangdong Kenuo Surveying Engineering Co., Ltd Guangzhou, China
Huaan Wang
Affiliation:
China Energy Engineering Group Guangdong Electric Power Design Institute Co., Ltd Guangzhou, China Guangdong Kenuo Surveying Engineering Co., Ltd Guangzhou, China
Kailong Mu
Affiliation:
College of Water Conservancy and Hydropower Engineering, Hohai University Nanjing, China
Lanhao Zhao
Affiliation:
College of Water Conservancy and Hydropower Engineering, Hohai University Nanjing, China
*
*Corresponding author ([email protected])
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Abstract

In order to maintain the no-slip condition and the divergence-free property simultaneously, an iterative scheme of immersed boundary method in the finite element framework is presented. In this method, the Characteristic-based Split scheme is employed to solve the momentum equations and the formulation for the pressure and the extra body force is derived according to the no-slip condition. The extra body force is divided into two divisions, one is in relation to the pressure and the other is irrelevant. Two corresponding independent iterations are set to solve the two sections. The novelty of this method lies in that the correction of the velocity increment is included in the calculation of the extra body force which is relevant to the pressure and the update of the force is incorporated into the iteration of the pressure. Hence, the divergence-free properties and no-slip conditions are ensured concurrently. In addition, the current method is validated with well-known benchmarks.

Keywords

immersed boundary methoditerative schemedivergence-freefinite element framework
Type
Research Article
Information
Journal of Mechanics , Volume 36 , Issue 6 , December 2020 , pp. 901 - 914
Copyright
Copyright © 2020 The Society of Theoretical and Applied Mechanics

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References

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