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We present a novel framework inspired by the Immersed Boundary Method for predicting the fluid-structure interaction of complex structures immersed in laminar, transitional and turbulent flows. The key elements of the proposed fluid-structure interaction framework are 1) the solution of elastodynamics equations for the structure, 2) the use of a high-order Navier–Stokes solver for the flow, and 3) the variational transfer (L 2-projection) for coupling the solid and fluid subproblems. The dynamic behavior of a deformable structure is simulated in a finite element framework by adopting a fully implicit scheme for its temporal integration. It allows for mechanical constitutive laws including inhomogeneous and fiber-reinforced materials. The Navier–Stokes equations for the incompressible flow are discretized with high-order finite differences which allow for the direct numerical simulation of laminar, transitional and turbulent …