Applications of the Immersed Element-Free Galerkin Method

Abstract

In this paper, we present a new numerical method, the Immersed Element-Free Galerkin Method (IEFGM), for the solution of fluid-structure interaction problems. The technique is a variation of the Immersed Finite Element Method developed by (L. Zhang et al., Journal of Fluids and Structures, 23(6):836-857 (2007)) in which the fluid-solid interaction force is represented as a volumetric force in the momentum equations. In IEFGM, a Lagrangian solid domain moves on top of an Eulerian fluid domain which spans over the entire computational region. In this work, the fluid (Eulerian) domain is modeled using the finite element method and the solid (Lagrangian) domain is modeled using the element-free Galerkin method. We assure the continuity between the solid and fluid domains by means of a local approximation, in the vicinity of the solid domain, of the velocity field and the fluid-structure interaction force. Such an approximation is achieved using the moving least squares (MLS) technique. The method is applied to simulating the motion of rigid and deformable objects falling in a viscous fluid. Good performance of the method is obtained when comparing simulated results with analytical solutions or published works using other numerical approaches. The method is currently being enhanced to simulate the transport of deformable inclusions in liquid metals.