A hybridizable discontinuous Galerkin method for modeling fluid–structure interaction

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

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

This work 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.

Original languageEnglish (US)
Pages (from-to)91-114
Number of pages24
JournalJournal of Computational Physics
Volume326
DOIs
StatePublished - Dec 1 2016

Fingerprint

Galerkin method
Galerkin methods
formulations
interactions
Elasticity
Physics
elastostatics
Fluids
elastodynamics
physics
fluids
mathematics
Polynomials
finite element method
polynomials
Finite element method
elastic properties
trends
simulation

All Science Journal Classification (ASJC) codes

  • Numerical Analysis
  • Modeling and Simulation
  • Physics and Astronomy (miscellaneous)
  • Physics and Astronomy(all)
  • Computer Science Applications
  • Computational Mathematics
  • Applied Mathematics

Cite this

@article{5f20f181e2684c2581ff5a862ea75e8f,
title = "A hybridizable discontinuous Galerkin method for modeling fluid–structure interaction",
abstract = "This work 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.",
author = "Sheldon, {Jason P.} and Miller, {Scott T.} and Pitt, {Jonathan S.}",
year = "2016",
month = "12",
day = "1",
doi = "10.1016/j.jcp.2016.08.037",
language = "English (US)",
volume = "326",
pages = "91--114",
journal = "Journal of Computational Physics",
issn = "0021-9991",
publisher = "Academic Press Inc.",

}

A hybridizable discontinuous Galerkin method for modeling fluid–structure interaction. / Sheldon, Jason P.; Miller, Scott T.; Pitt, Jonathan S.

In: Journal of Computational Physics, Vol. 326, 01.12.2016, p. 91-114.

Research output: Contribution to journalArticle

TY - JOUR

T1 - A hybridizable discontinuous Galerkin method for modeling fluid–structure interaction

AU - Sheldon, Jason P.

AU - Miller, Scott T.

AU - Pitt, Jonathan S.

PY - 2016/12/1

Y1 - 2016/12/1

N2 - This work 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.

AB - This work 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.

UR - http://www.scopus.com/inward/record.url?scp=84986293297&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84986293297&partnerID=8YFLogxK

U2 - 10.1016/j.jcp.2016.08.037

DO - 10.1016/j.jcp.2016.08.037

M3 - Article

AN - SCOPUS:84986293297

VL - 326

SP - 91

EP - 114

JO - Journal of Computational Physics

JF - Journal of Computational Physics

SN - 0021-9991

ER -