Journal
COMMUNICATIONS IN COMPUTATIONAL PHYSICS
Volume 18, Issue 4, Pages 1147-1180Publisher
GLOBAL SCIENCE PRESS
DOI: 10.4208/cicp.150115.170415s
Keywords
Immersogeometric analysis; fluid-structure interaction; isogeometric analysis; collocation; stabilized methods; augmented Lagrangian
Categories
Funding
- CSEM Graduate Fellowship
- ICES Postdoctoral Fellowship at the Institute for Computational Engineering and Sciences
- ARO grant [W911NF-14-1-0296]
Ask authors/readers for more resources
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.
Authors
I am an author on this paper
Click your name to claim this paper and add it to your profile.
Reviews
Recommended
No Data Available