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.
N1 - Funding Information:
J. Sheldon gratefully acknowledges financial support from Naval Sea Systems Command , Advanced Submarine Systems Development Office, Mr. Patrick Tyler ( SEA073 ). S. Miller and J. Pitt acknowledge internal support for this research from the Applied Research Laboratory at The Pennsylvania State University.
Publisher Copyright:
© 2016 Elsevier Inc.
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.
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U2 - 10.1016/j.jcp.2016.08.037
DO - 10.1016/j.jcp.2016.08.037
M3 - Article
AN - SCOPUS:84986293297
SN - 0021-9991
VL - 326
SP - 91
EP - 114
JO - Journal of Computational Physics
JF - Journal of Computational Physics
ER -