@Article{CiCP-18-1147,
author = {},
title = {Stability and Conservation Properties of Collocated Constraints in Immersogeometric Fluid-Thin Structure Interaction Analysis},
journal = {Communications in Computational Physics},
year = {2018},
volume = {18},
number = {4},
pages = {1147--1180},
abstract = {<p style="text-align: justify;">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, &quot;An immersogeometric variational
framework for fluid-structure interaction: Application to bioprosthetic heart valves&quot;,
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.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.150115.170415s},
url = {http://global-sci.org/intro/article_detail/cicp/11064.html}
}