An Immersed Smoothed Finite Element Method Combined with Hybridizable Discontinous Galerkin Method (IS-FEM-HDG) for Fluid-Structure Interaction

An immersed-type numerical method, so called IS-FEM-HDG, is implemented based on the Immersed Smoothed Finite Element Method (IS-FEM) and the Hybridizable Discontinous Galerkin Method (HDG), for 2D fluid-structure interaction (FSI) problems. The IS-FEM-HDG is constructed under the framework of the IS-FEM, which consists of three key modules: (1) the Smoothed Finite Element Method (S-FEM) to solve for the transient dynamics responses of the solids; (2) the HDG for analyzing the incompressible viscous fluid flow; (3) the immersed-type technique based on the fictitious fluid for the fluid-structure interactions. The accuracy and spatial convergence properties in the fluid solutions can be greatly improved in virtue of the advanced features of the HDG method, which are verified numerically. The HDG leads to the optimal κ+1 -th order spatial convergence rate in the fluid solutions if the κ-th order element is employed; and the S-FEM leads to the second order convergence rate in the solid solutions.