An immersed finite element method for interaction problems between rigid bodies and the incompressible Navier-Stokes flow

Abstract

Since the immersed boundary method (IBM) has been developed by C. Peskin to readily solve the fluid-structure interaction (FSI) problems such as heart simulation and valveless pumping, diverse kind of methods stimulated by the IBM have appear, for example, the immersed interface method (IIM) by R. LeVeque and Z. Li to improve accuracy, the ghost fluid method (GFM) by S. Oscher, and the fictitious domain method independently developed by Glowinski, etc. At that time, the immersed finite element method (IFEM) by W. K. Liu also has been on the stage, which could be viewed as the finite element (IFEM) version of IBM. One of the salient features of the IFEM is in the use of the reproducing kernel particle method (RKPM) which plays a similar role to the discrete Dirac delta function in IBM. It has advantages and at the same time disadvantages. On distributing the FSI force on the structure to the surrounding fluid, the RKPM is very easy to do that but it may spread out the FSI force to the fluid region larger than the structure domain. The support of such a spread FSI force apparently affects the accuracy of the numerical solution. In this talk, therefore, using the transformed finite element basis based on the Euler-Lagrange mapping, we can reduce the support size of the distributed FSI force on the fluid and hence we will show that the accuracy is able to be improved through the interaction problems of rigid bodies and the incompressible Navier-Stokes flow. We call this method the directly coupled Euler-Lagrange method (DCELM).