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

Abstract

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.

Authors:

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

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+ Show Author Affiliations

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

Publication Date:

Wed Aug 31 00:00:00 EDT 2016

Research Org.:

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

Sponsoring Org.:

USDOE National Nuclear Security Administration (NNSA)

OSTI Identifier:

1326055

Report Number(s):

SAND-2016-1207J
Journal ID: ISSN 0021-9991; 643561

Grant/Contract Number:  

AC04-94AL85000

Resource Type:

Accepted Manuscript

Journal Name:

Journal of Computational Physics

Additional Journal Information:

Journal Volume: 326; Journal Issue: C; Journal ID: ISSN 0021-9991

Publisher:

Elsevier

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