  A stable added-mass partitioned (AMP) algorithm is developed for
fluid-structure interaction (FSI) problems involving viscous incompressible
flow and compressible elastic solids. Deforming composite grids are used to
effectively handle the evolving geometry and large deformations. 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 new algorithm is verified for
accuracy and stability on a number of useful benchmark problems including a
radial-piston problem where exact solutions for radial and azimuthal motions
are found and tested. Traveling wave exact solutions are also derived and
numerically verified for a solid disk surrounded by an annulus of fluid. Fluid
flow in a channel past a deformable solid annulus is computed and errors are
estimated from a self-convergence grid refinement study. The AMP scheme is
found to be stable and second-order accurate even for very difficult cases of
very light solids.
