Immersed finite element method for fluid-structure interactions

In this paper, we present a detailed derivation of the numerical method, Immersed Finite Element Method (IFEM), for the solution of fluid-structure interaction problems. This method is developed based on the Immersed Boundary (IB) method that was initiated by Peskin, with additional capabilities in handling nonuniform and independent meshes and applying arbitrary boundary conditions on both fluid and solid domains. A higher order interpolation function is adopted from one of the mesh-free methods, the Reproducing Kernel Particle Method (RKPM), which relieves the uniformity constraint of fluid meshes. Two 2-D example problems are presented to illustrate the capabilities of the algorithm. The accuracy in the numerical analysis demonstrates that the IFEM algorithm is a reliable and robust numerical approach to solve fluid and deformable solid interactions.