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STABILIZED, MULTISCALE, AND MULTIPHYSICS METHODS IN FLUID MECHANICS

Added Mass Effects of Compressible and Incompressible Flows in Fluid-Structure Interaction

[+] Author and Article Information
E. H. van Brummelen

Faculty of Mechanical, Maritime and Materials Engineering, Delft University of Technology, Mekelweg 2, Delft, 2628 CD, Netherlandse.h.vanbrummelen@tudelft.nl

In principle, this statement requires somewhat more care because it is not a priori obvious that ϱi in Eq. 36 does not represent an upper bound attained in the limit ω. A more precise analysis of Eq. 35 with P̂ according to Eq. 33 reveals that this is not the case.

J. Appl. Mech 76(2), 021206 (Jan 15, 2009) (7 pages) doi:10.1115/1.3059565 History: Received December 04, 2007; Revised May 22, 2008; Published January 15, 2009

The subiteration method, which forms the basic iterative procedure for solving fluid-structure-interaction problems, is based on a partitioning of the fluid-structure system into a fluidic part and a structural part. In fluid-structure interaction, on short time scales the fluid appears as an added mass to the structural operator, and the stability and convergence properties of the subiteration process depend significantly on the ratio of this apparent added mass to the actual structural mass. In the present paper, we establish that the added-mass effects corresponding to compressible and incompressible flows are fundamentally different. For a model problem, we show that on increasingly small time intervals, the added mass of a compressible flow is proportional to the length of the time interval, whereas the added mass of an incompressible flow approaches a constant. We then consider the implications of this difference in proportionality for the stability and convergence properties of the subiteration process, and for the stability and accuracy of loosely coupled staggered time-integration methods.

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Copyright © 2009 by American Society of Mechanical Engineers
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Illustration of the panel problem: temporal cross section with expanded interface region

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