An immersed edge-based smoothed finite element method with the stabilized pressure gradient projection for fluid–structure interaction

Abstract

In this paper, an effective and stable immersed edge-based smoothed finite element method (IES-FEM) is presented for fluid–structure interaction (FSI) problems. Under the framework of immersed algorithm, the system equation can be decomposed into three components, i.e, equations of nonlinear structure, incompressible viscous fluid, and FSI force. The characteristic-based split (CBS) scheme is first used to alleviate the spatial oscillation in the Navier-Stokes (N-S) equation. After that, the second-order pressure accuracy is formulated in the original CBS via stabilized pressure gradient projection (SPGP). Then, the problem domains are discretized using the simplest three-node triangular element and the smoothing domains are established. In order to enhance the accuracy of lower-order interpolation, the edge-based smoothing operation is further performed on all gradient-related terms for structure and fluid, namely, the coupled ES/ES-FEM. Moreover, an accurate form of FSI force evaluation is developed by introducing the whole function that considers the pressure and viscous force on the interface. Numerical examples demonstrate that the proposed scheme has higher computational precision (even for distorted mesh), faster convergence rate, good robustness, and lower computed costs.