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The core of Computational Fluid Dynamics (CFD) is to transform complex fluid motion into a set of mathematical equations, and the mesh is the key step to discretize the continuous space, which directly determines the accuracy of the solution and the demand of computational resources. Traditional simple grids are difficult to accurately capture complex flow patterns and boundary effects, and unstructured grids are flexible but increase the algorithm complexity and computational cost. It is in this context that the existence of Cartesian grids has become an important weight in balancing the CFD simulation accuracy and efficiency scales. However, the due the limit of shape function, the Cartesian grid with hanging nodes (CGHN) was rarely used in finite element method (FEM) based CFD algorithm. This work developed a smoothed finite element method (S-FEM) based on CGHN meshes for the fluid-structure interaction problems in incompressible fluids and large deformed solids. The results of numerical examples show that the method proposed in this paper possesses high accuracy and robustness.

Cartesian grid with hanging nodes; Smoothed Finite Element Method; Computational Fluid Dynamics; Fluid-Structure Interaction; Gradient smoothing technique