Immersed finite element method

In this paper, the immersed finite element method (IFEM) is proposed for the solution of complex fluid and deformable structure interaction problems encountered in many physical models. In IFEM, a Lagrangian solid mesh moves on top of a background Eulerian fluid mesh which spans over the entire computational domain. Hence, the mesh generation is greatly simplified. Moreover, both fluid and solid domains are modeled with the finite element methods and the continuity between the fluid and solid sub-domains are enforced via the interpolation of the velocities and the distribution of the forces with the reproducing kernel particle method (RKPM) delta function. In comparison with the immersed boundary (IB) method, the higher-ordered RKPM delta function enables the fluid domain to have nonuniform spatial meshes with arbitrary geometries and boundary conditions. The use of such kernel functions may eventually open doors to multi-scale and multi-resolution modelings of complex fluid-structure interaction problems. Rigid and deformable spheres dropping in channels are simulated to demonstrate the unique capabilities of the proposed method. The results compare well with the experimental data. To the authors' knowledge, these are the first solutions that deal with particulate flows with very flexible solids.