Campus Units

Mechanical Engineering

Document Type

Article

Publication Version

Accepted Manuscript

Publication Date

10-2015

Journal or Book Title

Communications in Computational Physics

Volume

18

Issue

4

First Page

1147

Last Page

1180

DOI

10.4208/cicp.150115.170415s

Abstract

The purpose of this study is to enhance the stability properties of our recently-developed numerical method [D. Kamensky, M.-C. Hsu, D. Schillinger, J.A. Evans, A. Aggarwal, Y. Bazilevs, M.S. Sacks, T.J.R. Hughes, “An immersogeometric variational framework for fluid-structure interaction: Application to bioprosthetic heart valves”, Comput. Methods Appl. Mech. Engrg., 284 (2015) 1005–1053] for immersing spline-based representations of shell structures into unsteady viscous incompressible flows. In the cited work, we formulated the fluid-structure interaction (FSI) problem using an augmented Lagrangian to enforce kinematic constraints. We discretized this Lagrangian as a set of collocated constraints, at quadrature points of the surface integration rule for the immersed interface. Because the density of quadrature points is not controlled relative to the fluid discretization, the resulting semi-discrete problem may be over-constrained. Semi-implicit time integration circumvents this difficulty in the fully-discrete scheme. If this time-stepping algorithm is applied to fluid-structure systems that approach steady solutions, though, we find that spatially-oscillating modes of the Lagrange multiplier field can grow over time. In the present work, we stabilize the semi-implicit integration scheme to prevent potential divergence of the multiplier field as time goes to infinity. This stabilized time integration may also be applied in pseudo-time within each time step, giving rise to a fully implicit solution method. We discuss the theoretical implications of this stabilization scheme for several simplified model problems, then demonstrate its practical efficacy through numerical examples.

Comments

This is a manuscript of an article is published as D. Kamensky, J.A. Evans, M.-C. Hsu, “Stability and conservation properties of collocated constraints in immersogeometric fluid–thin structure interaction analysis,” Communications in Computational Physics, 18 (2015) 1147-1180. doi: https://doi.org/10.4208/cicp.150115.170415s. Posted with permission.

Copyright Owner

Global-Science Press

Language

en

File Format

application/pdf

Published Version

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