  We present a general simulation approach for incompressible fluid--structure
interactions in a fully Eulerian framework using the reference map technique
(RMT). The approach is suitable for modeling one or more rigid or
finitely-deformable objects or soft objects with rigid components interacting
with the fluid and with each other. It is also extended to control the
kinematics of structures in fluids. The model is based on our previous Eulerian
fluid--soft solver, and generalized to rigid structures by constraining the
deformation-rate tensor in a projection framework. Several numerical examples
are presented to illustrate the capability of the method.
