  We present an immersed boundary projection method formulated in a body-fixed
frame of reference for flow-structure interaction (FSI) problems involving
rigid bodies with complex geometries. The body-fixed formulation is aimed at
maximizing the accuracy of surface stresses on the FSI body (the target) on
during spatial and temporal discretization. The incompressible vorticity
equations and Newton's equations of motion are coupled implicitly so that the
method remains stable for low solid-to-fluid mass ratios. The influence of
fictitious fluid inside the rigid bodies is considered and the spurious
oscillations in surface stresses are filtered to impose physically correct
rigid body dynamics. Similar to many predecessors of the immersed boundary
projection method, the resulting discrete system is solved efficiently using a
block-LU decomposition. We then validate the method with two-dimensional test
problems of a neutrally buoyant cylinder migrating in a planar Couette flow and
a freely falling or rising cylindrical rigid body.
