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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| Vydané v: | Computer methods in applied mechanics and engineering Ročník 295; s. 172 - 195 |
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| Hlavní autori: | , , , |
| Médium: | Journal Article |
| Jazyk: | English |
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Elsevier B.V
01.10.2015
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| ISSN: | 0045-7825, 1879-2138 |
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| Abstract | 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. |
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| AbstractList | 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. |
| Author | Etienne, S. Pelletier, D. Hay, A. Garon, A. |
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| Cites_doi | 10.1002/fld.981 10.1007/BF01932401 10.1002/fld.3944 10.2307/2007989 10.1006/jcph.1996.0081 10.1016/j.jcp.2015.03.022 10.1016/j.cma.2009.10.005 10.1137/0711079 10.1137/0721048 10.1016/j.compfluid.2014.04.036 10.1007/BF01389580 10.1137/0903023 10.1016/j.jfluidstructs.2011.12.004 10.1016/j.jcp.2005.08.018 10.1137/080728032 |
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