In this article we describe a stable partitioned algorithm that overcomes the
added mass instability arising in fluid-structure interactions of light rigid
bodies and inviscid compressible flow. The new algorithm is stable even for
bodies with zero mass and zero moments of inertia. The approach is based on a
local characteristic projection of the force on the rigid body and is a natural
extension of the recently developed algorithm for coupling compressible flow
and deformable bodies. Normal mode analysis is used to prove the stability of
the approximation for a one-dimensional model problem and numerical
computations confirm these results. In multiple space dimensions the approach
naturally reveals the form of the added mass tensors in the equations governing
the motion of the rigid body. These tensors, which depend on certain surface
integrals of the fluid impedance, couple the translational and angular
velocities of the body. Numerical results in two space dimensions, based on the
use of moving overlapping grids and adaptive mesh refinement, demonstrate the
behavior and efficacy of the new scheme. These results include the simulation
of the difficult problem of a shock impacting an ellipse of zero mass.Comment: 32 pages, 20 figure