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.

中文翻译：

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用于二维流固耦合的保守浸入式算法和基于笛卡尔网格的平滑有限元方法


笛卡尔网格在计算流体动力学（CFD）中非常流行，具有网格质量高、易于生成的特点。然而，由于形状函数的限制，悬挂节点笛卡尔网格（CGHN）在基于有限元法的CFD算法中很少使用。基于浸入边界法的框架，针对不可压缩流体和大变形结构的流固耦合问题，提出了基于CGHN的平滑有限元方法。梯度平滑技术简化了悬挂节点的处理，保证了笛卡尔单元的网格密度。在求解非线性NS方程时，基于特征的分割格式与稳定压力梯度投影相结合，克服了类Galerkin方法中的对流和压力振荡。异构网格映射技术是为流体域和固体域之间的数据传输而开发的。开发了一种高效、准确和广义的质量守恒算法来解决流体和固体之间数据传输中的压力振荡。算例结果表明该方法具有较高的精度和鲁棒性。