The stabilization-free HDG method for fluid-structure interaction in a unified mixed formulation on Alfeld splits
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- by Eric Chung and Lina Zhao;
- Math. Comp. 94 (2025), 1633-1665
- DOI: https://doi.org/10.1090/mcom/4009
- Published electronically: August 16, 2024
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Abstract:
In this paper we propose and analyze a stabilization-free hybridizable discontinuous Galerkin (HDG) method in stress-velocity formulation for fluid-structure interaction based on Alfeld splits. A unified mixed formulation is employed for the Stokes equations and the elastodynamic equations. We use the standard polynomial space with strong symmetry to define the stress space, and use the broken $H(div;\Omega$)-conforming space of the same degree to define the vector space in a careful way such that the resulting scheme is stable without resorting to any stabilization. In particular, the proposed scheme addresses the pressure-robustness, which is known to be important for incompressible flows. The transmission conditions can be incorporated naturally without resorting to additional variables or Nitsche-type stabilization owing to the bespoke construction of the discrete formulation. To show the optimal convergence, we establish a new projection operator for the stress space whose definition accounts for traces of the method. Furthermore, the pressure-independence and the robustness with respect to fluid viscosity and the Lamé constants are investigated. We also show the characterization of the hybridization and the size of the global system is greatly reduced, rendering the scheme computationally attractive. Several numerical experiments are presented to verify the proposed theories.References
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Bibliographic Information
- Eric Chung
- Affiliation: Department of Mathematics, the Chinese University of Hong Kong, Hong Kong SAR, People’s Republic of China
- MR Author ID: 683572
- ORCID: 0000-0002-3096-3399
- Email: tschung@math.cuhk.edu.hk
- Lina Zhao
- Affiliation: Department of Mathematics, City University of Hong Kong, Kowloon Tong, Hong Kong SAR, People’s Reuplic of China
- MR Author ID: 1266544
- ORCID: 0000-0002-9606-8231
- Email: linazha@cityu.edu.hk
- Received by editor(s): March 7, 2024
- Received by editor(s) in revised form: July 16, 2024
- Published electronically: August 16, 2024
- Additional Notes: The research of the first author was partially supported by the Hong Kong RGC General Research Fund (Project: 14304021) and the research of the second author was partially supported by the Research Grants Council of the Hong Kong Special Administrative Region, China. (Project No. CityU 21309522).
The second author is the corresponding author - © Copyright 2024 American Mathematical Society
- Journal: Math. Comp. 94 (2025), 1633-1665
- MSC (2020): Primary 11Y60, 46N10; Secondary 65E05
- DOI: https://doi.org/10.1090/mcom/4009