Numerical stabilities of loosely coupled methods for robust modeling of lightweight and flexible structures in incompressible and viscous flows

Deniz Tolga Akcabay; Jian Xiao; Yin Lu Young

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Numerical stabilities of loosely coupled methods for robust modeling of lightweight and flexible structures in incompressible and viscous flows

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The growing interest to examine the hydroelastic dynamics and stabilities of lightweight and flexible materials requires robust and accurate fluid–structure interaction (FSI) models. Classically, partitioned fluid and structure solvers are easier to implement compared to monolithic methods;however, partitioned FSI models are vulnerable to numerical ("virtual added mass") instabilities for cases when the solid to fluid density ratio is low and if the flow is incompressible. As a partitioned method, the loosely hybrid coupled (LHC) method, which was introduced and validated in Young et al. (Acta Mech. Sin. 28:1030–1041, 2012), has been success-fully used to efficiently and stably model lightweight and flexible structures. The LHC method achieves its numerical stability by, in addition to the viscous fluid forces, embed-ding potential flow approximations of the fluid induced forces to transform the partitioned FSI model into a semi-implicit scheme. The objective of this work is to derive and validate the numerical stability boundary of the LHC. The results show that the stability boundary of the LHC is much wider than traditional loosely coupled methods for a variety of numerical integration schemes. The results also show that inclusion of an estimate of the fluid inertial forces is the most critical to ensure the numerical stability when solving for fluid–structure interaction problems involving cases with a solid to fluid-added mass ratio less than one.

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《力学学报：英文版》 |2017年第004期|709-724|共16页
作者
Deniz Tolga Akcabay; Jian Xiao; Yin Lu Young;
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Department of Naval Architecture and Marine Engineering, University of Michigan, 2600 Draper Dr., Ann Arbor, MI 48109-2145, USA;

Department of Naval Architecture and Marine Engineering, University of Michigan, 2600 Draper Dr., Ann Arbor, MI 48109-2145, USA;

Department of Naval Architecture and Marine Engineering, University of Michigan, 2600 Draper Dr., Ann Arbor, MI 48109-2145, USA;

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Numerical stabilities of loosely coupled methods for robust modeling of lightweight and flexible structures in incompressible and viscous flows

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