An immersed transitional interface finite element method for fluid interacting with rigid/deformable solid

An immersed transitional interface finite element method (ITI-FEM) is proposed to simulate fluid-structure interaction (FSI). In the framework of finite element method (FEM), the Navier-Stokes equations and the dynamic equation for solid are integrated using the Galerkin method, and the velocity and traction of the fluid are interpolated with those of the solid using the finite element interpolation function. Since the immersed finite element method (IFEM) generates an unphysical velocity/pressure field within the overlapping fluid domain that leads to possible accumulative errors and difficulties in convergence, a ghost fluid domain is introduced to replace the unphysical domain so that the unphysical fluid velocity and pressure are not involved in the equations of the FSI system. A transitional interface is then established to smooth the oscillating solution, along with a momentum-forcing term incorporated into its N-S equations to compensate for the induced errors. Without the inference from the unphysical velocity/pressure, the ITI-FEM has good robustness and accuracy. To validate the proposed ITI-IFEM, a flow over a stationary solid at two different Reynolds numbers and a flow over a moving rigid solid are simulated, examples of the flow-induced interaction with small deformation and finite deformation are also given. The calculated results generally agree with the published results. The proposed method exhibits good capabilities in bio-mechanical engineering application.