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A semi-implicit finite element formulation of the partitioned method for fluid-structure interaction based on a flux boundary condition of pressure equation

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Abstract

A semi-implicit algorithm of the partitioned method is newly proposed for fluid-structure interaction using the finite element method. In particular, an incompressible fluid flow is solved by a splitting method, and the solid domain of a reference configuration is solved by a total Lagrangian approach. While the viscous traction of the fluid flow is explicitly estimated in a coupling algorithm, the pressure traction from the fluid flow is implicitly coupled with the solid motion through iterative computations separately performed on the fluid and then the solid domain. By employing a weak formulation of the pressure Poisson equation based on a flux (fluid velocity) boundary condition, solid motion is successfully coupled with the pressure equation during the iterative computation. The proposed method has been found to be more efficient compared with not only a fully-implicit scheme of the partitioned method, but also a monolithic formulation in terms of CPU time and memory usage. Lastly, the parallel implementation of the proposed method is very attractive due to the fluid-solid coupling through a simple pressure Poisson equation.

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Acknowledgments

This study was supported by the Basic Science Research Program (2020R1I1A3066617) from the National Research Foundation of Korea (NRF).

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Authors and Affiliations

  1. Department of Mechanical Engineering, Le Quy Don Technical University, Hanoi, Vietnam

    Sang Truong Ha

  2. Department of Mechanical and Automotive Engineering, Seoul National University of Science and Technology, Seoul, 01811, Korea

    Hyoung Gwon Choi

  3. School of Mechanical Engineering, University of Ulsan, Ulsan, 44610, Korea

    Ngo Cu Long & Sang-Wook Lee

Authors
  1. Sang Truong Ha
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  2. Hyoung Gwon Choi
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  3. Ngo Cu Long
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  4. Sang-Wook Lee
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Corresponding author

Correspondence to Sang-Wook Lee.

Additional information

S. T. Ha is a researcher in Mechanical Engineering at Le Quy Don Technical University, Ha Noi, Viet Nam. His Ph.D. in Mechanical Engineering is from Seoul National University of Science and Technology. His research interests include computational fluid dynamics, fluid-structure interaction and multi-grid method.

L. C. Ngo is a postdoctoral fellow in Mechanical Engineering at the University of Ulsan. His Ph.D. in Mechanical Engineering is from Seoul National University of Science and Technology, Korea. His research interests include numerical methods for multiphase flows such as finite element method and level set method.

H. G. Choi is a Professor of Mechanical/Automotive Engineering, Seoul National University of Science and Technology. His Ph.D. is from Seoul National University, Korea. His research interests include finite element method, level set method and fluid-structure interaction.

S.-W. Lee received his Ph.D. in Mechanical Engineering from the University of Illinois at Chicago in 2005. Currently, he is a Professor of Mechanical Engineering at the University of Ulsan. His research interests include cardiovascular mechanics and computational fluid dynamics.

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Ha, S.T., Choi, H.G., Long, N.C. et al. A semi-implicit finite element formulation of the partitioned method for fluid-structure interaction based on a flux boundary condition of pressure equation. J Mech Sci Technol 37, 2417–2424 (2023). https://doi.org/10.1007/s12206-023-0418-5

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  • DOI: https://doi.org/10.1007/s12206-023-0418-5

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