We present a general simulation approach for incompressible fluid–structure interactions in a fully Eulerian framework using the reference map technique. 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 [Rycroft et al., “Reference map technique for incompressible fluid–structure interaction,” J. Fluid Mech. 898, A9 (2020)] 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.
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