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A stable partitioned algorithm is developed for fluid-structure interaction(FSI) problems involving viscous incompressible flow and rigid bodies. This{\em added-mass partitioned} (AMP) algorithm remains stable, withoutsub-iterations, for light and even zero mass rigid bodies when added-mass andviscous added-damping effects are large. The scheme is based on a generalizedRobin interface condition for the fluid pressure that includes terms involvingthe linear acceleration and angular acceleration of the rigid body. Added-masseffects are handled in the Robin condition by inclusion of a boundary integralterm that depends on the pressure. Added-damping effects due to the viscousshear forces on the body are treated by inclusion of added-damping tensors thatare derived through a linearization of the integrals defining the force andtorque. Added-damping effects may be important at low Reynolds number, or, forexample, in the case of a rotating cylinder or rotating sphere when therotational moments of inertia are small. In this first part of a two-partseries, the properties of the AMP scheme are motivated and evaluated throughthe development and analysis of some model problems. The analysis shows whenand why the traditional partitioned scheme becomes unstable due to eitheradded-mass or added-damping effects. The analysis also identifies the properform of the added-damping which depends on the discrete time-step and thegrid-spacing normal to the rigid body. The results of the analysis areconfirmed with numerical simulations that also demonstrate a second-orderaccurate implementation of the AMP scheme.

A stable partitioned FSI algorithm for rigid bodies and incompressible flow. Part I: Model problem analysis