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Volume 20, Issue 2
Monolithic and Partitioned Finite Element Schemes for FSI Based on an ALE Divergence-Free HDG Fluid Solver and a TDNNS Structural Solver

Guosheng Fu

DOI: 10.4208/ijnam2023-1011

Int. J. Numer. Anal. Mod., 20 (2023), pp. 267-312.

Published online: 2023-01

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  • Abstract

We present novel (high-order) finite element schemes for the fluid-structure interaction (FSI) problem based on an arbitrary Lagrangian-Eulerian divergence-free hybridizable discontinuous Gakerkin (ALE divergence-free HDG) incompressible flow solver, a Tangential-Displacement-Normal-Normal-Stress (TDNNS) nonlinear elasticity solver, and a generalized Robin interface condition treatment. Temporal discretization is performed using the high-order backward difference formulas (BDFs). Both monolithic and strongly coupled partitioned fully discrete schemes are obtained. Numerical convergence studies are performed for the flow and elasticity solvers, and the coupled FSI solver, which verify the high-order space-time convergence of the proposed schemes. Numerical results on classical two dimensional benchmark problems also showed good performance of our proposed methods.

  • Keywords

Divergence-free HDG, ALE, FSI, TDNNS, generalized Robin condition, partitioned scheme.

  • AMS Subject Headings

65N30, 65N12, 76S05, 76D07

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-20-267, author = {Fu , Guosheng}, title = {Monolithic and Partitioned Finite Element Schemes for FSI Based on an ALE Divergence-Free HDG Fluid Solver and a TDNNS Structural Solver}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2023}, volume = {20}, number = {2}, pages = {267--312}, abstract = {

We present novel (high-order) finite element schemes for the fluid-structure interaction (FSI) problem based on an arbitrary Lagrangian-Eulerian divergence-free hybridizable discontinuous Gakerkin (ALE divergence-free HDG) incompressible flow solver, a Tangential-Displacement-Normal-Normal-Stress (TDNNS) nonlinear elasticity solver, and a generalized Robin interface condition treatment. Temporal discretization is performed using the high-order backward difference formulas (BDFs). Both monolithic and strongly coupled partitioned fully discrete schemes are obtained. Numerical convergence studies are performed for the flow and elasticity solvers, and the coupled FSI solver, which verify the high-order space-time convergence of the proposed schemes. Numerical results on classical two dimensional benchmark problems also showed good performance of our proposed methods.

}, issn = {2617-8710}, doi = {https://doi.org/10.4208/ijnam2023-1011}, url = {http://global-sci.org/intro/article_detail/ijnam/21361.html} }
TY - JOUR T1 - Monolithic and Partitioned Finite Element Schemes for FSI Based on an ALE Divergence-Free HDG Fluid Solver and a TDNNS Structural Solver AU - Fu , Guosheng JO - International Journal of Numerical Analysis and Modeling VL - 2 SP - 267 EP - 312 PY - 2023 DA - 2023/01 SN - 20 DO - http://doi.org/10.4208/ijnam2023-1011 UR - https://global-sci.org/intro/article_detail/ijnam/21361.html KW - Divergence-free HDG, ALE, FSI, TDNNS, generalized Robin condition, partitioned scheme. AB -

We present novel (high-order) finite element schemes for the fluid-structure interaction (FSI) problem based on an arbitrary Lagrangian-Eulerian divergence-free hybridizable discontinuous Gakerkin (ALE divergence-free HDG) incompressible flow solver, a Tangential-Displacement-Normal-Normal-Stress (TDNNS) nonlinear elasticity solver, and a generalized Robin interface condition treatment. Temporal discretization is performed using the high-order backward difference formulas (BDFs). Both monolithic and strongly coupled partitioned fully discrete schemes are obtained. Numerical convergence studies are performed for the flow and elasticity solvers, and the coupled FSI solver, which verify the high-order space-time convergence of the proposed schemes. Numerical results on classical two dimensional benchmark problems also showed good performance of our proposed methods.

Fu , Guosheng. (2023). Monolithic and Partitioned Finite Element Schemes for FSI Based on an ALE Divergence-Free HDG Fluid Solver and a TDNNS Structural Solver. International Journal of Numerical Analysis and Modeling. 20 (2). 267-312. doi:10.4208/ijnam2023-1011
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