Time-integration for ALE simulations of Fluid–Structure Interaction problems: Stepsize and order selection based on the BDF

We present an adaptive algorithm for time integration of fluid–structure integration problems. The method relies on a fully coupled procedure to solve FSI problems in which a naturally GCL-compliant ALE formulation for the finite-element spatial discretization is used. The main originality of the pr...

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Bibliographic Details
Published in:Computer methods in applied mechanics and engineering Vol. 295; pp. 172 - 195
Main Authors: Hay, A., Etienne, S., Garon, A., Pelletier, D.
Format: Journal Article
Language:English
Published: Elsevier B.V 01.10.2015
Subjects:
Adaptivity
Arbitrary Eulerian Lagrangian
Fluid–Structure Interaction
Time integration
Vortex induced vibration
Wake induced vibration
Arbitrary Eulerian Lagrangian
Adaptivity
Wake induced vibration
Vortex induced vibration
Fluid–Structure Interaction
Time integration
ISSN:0045-7825, 1879-2138
Online Access:Get full text
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Summary:We present an adaptive algorithm for time integration of fluid–structure integration problems. The method relies on a fully coupled procedure to solve FSI problems in which a naturally GCL-compliant ALE formulation for the finite-element spatial discretization is used. The main originality of the proposed solution procedure is that time integration is performed using automatic order and stepsize selections (hp-adaptivity) based on the Backward Differentiation Formulas (BDF). The stepsize selection is based on a local error estimate, an error controller and a step rejection mechanism. It guarantees that the solution precision is within the user targeted tolerance. The order selection is based on a stability test and a quarantine mechanism. The selection is performed to ensure that no other methods within the family of 0-stable BDF methods would produce a solution of the targeted precision for a larger stepsize (and thus a lower computational time). To improve efficiency, the time integration procedure also relies on a modified Newton method and a predictor. The time adaptive algorithm behaviors and performances are assessed on the vortex-induced translational and rotational vibrations of a square cylinder and on the wake-induced vibrations of 3 cylinders in an in-line arrangement. The algorithm yields substantial CPU time savings (compared to constant stepsize and order integration) while delivering solutions of prescribed accuracies.
ISSN:0045-7825
1879-2138
DOI:10.1016/j.cma.2015.06.006