The subiteration method which forms the basic iterative procedure for solving fluid-structureinteraction 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 timeintegration methods.

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SUMMARYThe numerical solution of uid-structure interactions with the customary subiteration method incurs numerous deÿciencies. We propose a novel solution method based on the conjugation of subiteration with a Newton-Krylov method, and demonstrate its superiority and beneÿcial characteristics.

SUMMARYThe basic subiteration method for fluid-structure interaction (FSI) problems is based on a partitioning of the fluid-structure system into a fluidic part and a structural part. The effect of the fluid on the structure can be represented by an added mass to the structural operator. This added mass can be identified as an upper bound on the norm or spectral radius of the Poincaré-Steklov operator of the fluid. The convergence behavior of the subiteration method depends sensitively on the ratio of the added mass to the actual structural mass. For FSI problems with large added-mass effects, the subiteration method is either unstable or its convergence behavior is prohibitively inefficient. In recent years, several more advanced partitioned iterative solution methods have been proposed for this class of problems, which use subiteration as a component. The rudimentary characterization of the Poincaré-Steklov operator provided by the added mass is, however, inadequate to analyze these methods. Moreover, this characterization is inappropriate for compressible flows. In this paper, we investigate the fine properties of the Poincaré-Steklov operators and of the corresponding subiteration operators for incompressible-and compressible flow models and for two distinct structural operators. Based on the characteristic properties of the subiteration operators, we subsequently examine the convergence behavior of several partitioned iterative solution methods for FSI, viz. subiteration, subiteration in conjunction with underrelaxation, the modified-mass method, Aitken's method, and interface-GMRES and interface-Newton-Krylov methods.

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