A hybridizable discontinuous Galerkin method for modeling fluid–structure interaction

Sheldon, Jason P.; Miller, Scott T.; Pitt, Jonathan S.

doi:10.1016/j.jcp.2016.08.037

Title: A hybridizable discontinuous Galerkin method for modeling fluid–structure interaction

Journal Article · Wed Aug 31 00:00:00 EDT 2016 · Journal of Computational Physics

DOI:https://doi.org/10.1016/j.jcp.2016.08.037· OSTI ID:1326055

Sheldon, Jason P. ^[1]; Miller, Scott T. ^[2]; Pitt, Jonathan S. ^[1]

The Pennsylvania State Univ., University Park, PA (United States)
Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

This study presents a novel application of the hybridizable discontinuous Galerkin (HDG) finite element method to the multi-physics simulation of coupled fluid–structure interaction (FSI) problems. Recent applications of the HDG method have primarily been for single-physics problems including both solids and fluids, which are necessary building blocks for FSI modeling. Utilizing these established models, HDG formulations for linear elastostatics, a nonlinear elastodynamic model, and arbitrary Lagrangian–Eulerian Navier–Stokes are derived. The elasticity formulations are written in a Lagrangian reference frame, with the nonlinear formulation restricted to hyperelastic materials. With these individual solid and fluid formulations, the remaining challenge in FSI modeling is coupling together their disparate mathematics on the fluid–solid interface. This coupling is presented, along with the resultant HDG FSI formulation. Verification of the component models, through the method of manufactured solutions, is performed and each model is shown to converge at the expected rate. The individual components, along with the complete FSI model, are then compared to the benchmark problems proposed by Turek and Hron [1]. The solutions from the HDG formulation presented in this work trend towards the benchmark as the spatial polynomial order and the temporal order of integration are increased.

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Research Organization:: Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

Sponsoring Organization:: USDOE National Nuclear Security Administration (NNSA)

Grant/Contract Number:: AC04-94AL85000

OSTI ID:: 1326055

Report Number(s):: SAND-2016-1207J; 643561

Journal Information:: Journal of Computational Physics, Vol. 326, Issue C; ISSN 0021-9991

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 16 works

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Discontinuous Galerkin approximations in computational mechanics: hybridization, exact geometry and degree adaptivity Giacomini, Matteo; Sevilla, Ruben SN Applied Sciences, Vol. 1, Issue 9 https://doi.org/10.1007/s42452-019-1065-4	journal	August 2019
An energy‐based discontinuous Galerkin method for coupled elasto‐acoustic wave equations in second‐order form Appelö, Daniel; Wang, Siyang International Journal for Numerical Methods in Engineering, Vol. 119, Issue 7 https://doi.org/10.1002/nme.6065	journal	April 2019
Hybridized Discontinuous Galerkin Methods for Wave Propagation Fernandez, P.; Christophe, A.; Terrana, S. Journal of Scientific Computing, Vol. 77, Issue 3 https://doi.org/10.1007/s10915-018-0811-x	journal	September 2018
Discontinuous Galerkin approximations in computational mechanics: hybridization, exact geometry and degree adaptivity Giacomini, Matteo; Sevilla, Ruben arXiv https://doi.org/10.48550/arxiv.1908.06604	text	January 2019

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Title: A hybridizable discontinuous Galerkin method for modeling fluid–structure interaction

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