A fully cell-based immersed smoothed finite element method with the mean value coordinate projection using quadrilateral elements for fluid-structure interaction

Abstract

In this work, an effective and stable immersed cell-based smoothed finite element method (ICS-FEM) together with mean value coordinate (MVC) projection using quadrilateral elements is presented for 2D fluid-structure interaction (FSI) problems. In an immersed-based algorithm, the entire system can be divided into three components: large-deformed nonlinear structure, incompressible viscous fluid, and fictitious fluid for FSI force. A characteristic-based split (CBS) CS-FEM solver is developed to solve the Navier-Stokes (N-S) equation. An explicit total Lagrange (TL) CS-FEM solver is utilized to depict the large deformation of the elastic structure. The problem domains are discretized into a set of quadrilateral elements and four cell-based smoothing domains are constructed for each element. The cell-based smoothing operation instead of the traditional mapping operation of isoparametric elements is executed to all gradient-related terms for both structures and fluids. A method based on the mean value coordinates is used for the interpolation process and the search criterion. Four numerical examples are utilized to illustrate the advance of the proposed method, including computational precision, convergence rate, robustness, etc.