Immersed finite element method for rigid body motions in the incompressible Navier-Stokes flow

The immersed finite element method (IFEM) takes places as a method developed for the purpose of solving effectively fluid-structure interaction problems including multi-physics ones. In the original IFEM, the reproducing kernel particle method (RKPM) playing a role of discrete Dirac delta function is employed to distribute the interacting force on the structure to the surrounding fluid and calculate the velocity on the structure induced from the background fluid. In this paper, fluid-structure interaction (FSI) problems in 2D between the incompressible Navier-Stokes flow and rigid structure are considered and we make use of the transformed finite element basis functions to replace discrete Dirac delta functions such as RKPM. This replacement makes the numerical support of FSI force distributed to the fluid smaller than that in case where the discrete Dirac delta function is used. In the finite element formulation, reducing the support size of distributed FSI force affects the accuracy of numerical solutions near the structure. The comparison of our numerical solution for particulate flows shows this fact well. We calculate particulate flows of rigid circular and rod type disks and compare them with the preceding results of reliability to show a good agreement to them. Moreover, the interaction motion for rod type of rigid structure in the fluid is traced.