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A stable added-mass partitioned (AMP) algorithm is developed forfluid-structure interaction (FSI) problems involving viscous incompressibleflow and compressible elastic-solids. The AMP scheme remains stable andsecond-order accurate even when added-mass and added-damping effects are large.The fluid is updated with an implicit-explicit (IMEX) fractional-step schemewhereby the velocity is advanced in one step, treating the viscous termsimplicitly, and the pressure is computed in a second step. The AMP interfaceconditions for the fluid arise from the outgoing characteristic variables inthe solid and are partitioned into a Robin (mixed) interface condition for thepressure, and interface conditions for the velocity. The latter conditionsinclude an impedance-weighted average between fluid and solid velocities usinga fluid impedance of a special form. A similar impedance-weighted average isused to define interface values for the solid. The fluid impedance is definedusing material and discretization parameters and follows from a carefulanalysis of the discretization of the governing equations and couplingconditions near the interface. A normal mode analysis is performed to show thatthe AMP scheme is stable for a few carefully-selected model problems. Twoextensions of the analysis in Banks et al. are considered, including afirst-order accurate discretization of a viscous model problem and asecond-order accurate discretization of an inviscid model problem. The AMPalgorithm is shown to be stable for any ratio of solid and fluid densities,including when added-mass effects are large. The algorithm is verified foraccuracy and stability for a set of new exact benchmark solutions where finiteinterface deformations are permitted. The AMP scheme is found to be stable andsecond-order accurate even for very difficult cases of very light solids.

A stable added-mass partitioned (AMP) algorithm for elastic solids and incompressible flow: model problem analysis