  A stable added-mass partitioned (AMP) algorithm is developed for
fluid-structure interaction (FSI) problems involving viscous incompressible
flow and compressible elastic-solids. The AMP scheme remains stable and
second-order accurate even when added-mass and added-damping effects are large.
The fluid is updated with an implicit-explicit (IMEX) fractional-step scheme
whereby the velocity is advanced in one step, treating the viscous terms
implicitly, and the pressure is computed in a second step. The AMP interface
conditions for the fluid arise from the outgoing characteristic variables in
the solid and are partitioned into a Robin (mixed) interface condition for the
pressure, and interface conditions for the velocity. The latter conditions
include an impedance-weighted average between fluid and solid velocities using
a fluid impedance of a special form. A similar impedance-weighted average is
used to define interface values for the solid. The fluid impedance is defined
using material and discretization parameters and follows from a careful
analysis of the discretization of the governing equations and coupling
conditions near the interface. A normal mode analysis is performed to show that
the AMP scheme is stable for a few carefully-selected model problems. Two
extensions of the analysis in Banks et al. are considered, including a
first-order accurate discretization of a viscous model problem and a
second-order accurate discretization of an inviscid model problem. The AMP
algorithm is shown to be stable for any ratio of solid and fluid densities,
including when added-mass effects are large. The algorithm is verified for
accuracy and stability for a set of new exact benchmark solutions where finite
interface deformations are permitted. The AMP scheme is found to be stable and
second-order accurate even for very difficult cases of very light solids.
