A hybridizable discontinuous Galerkin method for modeling fluid–structure interaction
This study presents a novel application of the hybridizable discontinuous Galerkin (HDG) finite element method to the multiphysics simulation of coupled fluid–structure interaction (FSI) problems. Recent applications of the HDG method have primarily been for singlephysics 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.
 Authors:

^{[1]};
^{[2]};
^{[1]}
 The Pennsylvania State Univ., University Park, PA (United States)
 Sandia National Lab. (SNLNM), Albuquerque, NM (United States)
 Publication Date:
 Report Number(s):
 SAND20161207J
Journal ID: ISSN 00219991; 643561
 Grant/Contract Number:
 AC0494AL85000
 Type:
 Accepted Manuscript
 Journal Name:
 Journal of Computational Physics
 Additional Journal Information:
 Journal Volume: 326; Journal Issue: C; Journal ID: ISSN 00219991
 Publisher:
 Elsevier
 Research Org:
 Sandia National Lab. (SNLNM), Albuquerque, NM (United States)
 Sponsoring Org:
 USDOE National Nuclear Security Administration (NNSA)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 97 MATHEMATICS AND COMPUTING; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; hybridizable discontinuous Galerkin; fluid–structure interaction; HDG FSI; monolithic coupling; arbitrary Lagrangian–Eulerian Navier–Stokes; elastodynamics
 OSTI Identifier:
 1326055
Sheldon, Jason P., Miller, Scott T., and Pitt, Jonathan S.. A hybridizable discontinuous Galerkin method for modeling fluid–structure interaction. United States: N. p.,
Web. doi:10.1016/j.jcp.2016.08.037.
Sheldon, Jason P., Miller, Scott T., & Pitt, Jonathan S.. A hybridizable discontinuous Galerkin method for modeling fluid–structure interaction. United States. doi:10.1016/j.jcp.2016.08.037.
Sheldon, Jason P., Miller, Scott T., and Pitt, Jonathan S.. 2016.
"A hybridizable discontinuous Galerkin method for modeling fluid–structure interaction". United States.
doi:10.1016/j.jcp.2016.08.037. https://www.osti.gov/servlets/purl/1326055.
@article{osti_1326055,
title = {A hybridizable discontinuous Galerkin method for modeling fluid–structure interaction},
author = {Sheldon, Jason P. and Miller, Scott T. and Pitt, Jonathan S.},
abstractNote = {This study presents a novel application of the hybridizable discontinuous Galerkin (HDG) finite element method to the multiphysics simulation of coupled fluid–structure interaction (FSI) problems. Recent applications of the HDG method have primarily been for singlephysics 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.},
doi = {10.1016/j.jcp.2016.08.037},
journal = {Journal of Computational Physics},
number = C,
volume = 326,
place = {United States},
year = {2016},
month = {8}
}