Smoothed finite element method for analysis of fluid-solid interaction problems

Abstract

The numerical method based on the cell-based smoothed finite element method is proposed to analyze fluid-solid interaction problems. Applying the gradient smoothing technique to the fluid and solid domain, fully-coupled FSI formulation is achieved, and the analysis is performed by means of polygonal and polyhedral elements. The element shape function based on the linear point interpolation method leads to simple element formulation and a good geometric adaptability. Due to the properties of the smoothed finite element method, it is possible to connect non-matching meshes along the fluid-solid interface by polygonal and polyhedral elements. The smoothed finite element method provides seamless connection without overlapping or gap satisfying the interfacial conditions of continuity, compatibility, and force equilibrium, which is verified through several patch tests. In addition, the performances of the solution including the accuracy and convergence behavior are demonstrated through several numerical examples. As a result, the proposed scheme based on the cell-based smoothed finite element method yields solutions of better accuracy and faster convergence rate than those of the conventional finite element method. Next, effective treatments for dealing with moving boundaries in FSI problems are proposed in the frame of local remeshing. For the two-dimensional problem, the sliding polygonal mesh method is suggested to overcome the problems of mesh distortion. For the three-dimensional problem, a new scheme is developed by adopting a surrounding cell around a solid in order to solve problems with a freely moving particle in the fluid. The validity of the proposed schemes is verified in comparison with the previous works, and the schemes provide good solutions.