Conservative immersed-type algorithm with a Cartesian grid-based smoothed finite element method for the 2D fluid-structure interaction

The Cartesian grid, which is highly popular in Computational Fluid Dynamics (CFD), has the characteristics of high mesh quality and easy generation. However, due to the limit of shape functions, the Cartesian grid with hanging nodes (CGHN) was rarely used in finite element method based CFD algorithm. Based on the framework of the immersed boundary method, a smoothed finite element method based on CGHN is developed for the fluid-structure interaction problems in incompressible fluids and large deformed structures. The gradient smoothing technique simplifies the processing of the hanging nodes and ensures the mesh density of the Cartesian elements. When solving the nonlinear N-S equations, the characteristic-based split format is combined with the stabilized pressure gradient projection to overcome the convection and pressure oscillations in the Galerkin-like method. A heterogeneous mesh mapping technology is developed for the data transfer between fluid and solid domains. An efficient, accurate and generalized mass conservation algorithm is developed to solve the pressure oscillations in data transfer between fluids and solids. The results of numerical examples show that the presented method possesses high accuracy and robustness.