I am seeking to perform fluid-structure interaction simulations by coupling a fluid and a structures code. I recently read a paper which highlighted an "added mass" error which can occur when coupling an incompressible fluid solver to a structural solver (although it does not occur in the compressible case), but did not explain this error further. Whould anyone be able to highlight how this error occurs?

You might want to start by thinking in terms of a simpler problem, the dynamics of a single rigid sphere immersed in a fluid. The added mass effect is just one of several messy terms that appear in the equation of motion, and all of this is explained in many of the classical fluids books. You just need to keep looking until you find one that goes beyond the usual drag coefficient.

Which text in particular would you recommend?