In this paper, a cell-based smoothed finite element method using the arbitrary n-sided polygonal element (CS-FEM-Poly) is developed to solve fluid mechanics problems. A stabilization method, characteristic-based split coupled with stabilized pressure gradient projection (CBS/SPGP), is employed to deal with numerical oscillations for CS-FEM-Poly. We validate CS-FEM-Poly and test its numerical behaviors using triangular, quadrilateral and polygonal elements on four typical numerical examples. Numerical results show that the CS-FEM-Poly based on CBS/SPGP produces well-agreed solutions with the exact solutions of benchmarks, and gives desirable convergence rate as compared with FEM. In the backward-facing step flow example, the numerical robustness for concave elements is manifested for CS-FEM-Poly. The proposed CS-FEM-Poly exhibits the remarkable potential for polygonal mesh or glued polygonal elements in the hybrid mesh to solve incompressible flows.

中文翻译：

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任意多边形单元求解不可压缩层流的基于元胞的平滑有限元法

在本文中，基于单元的平滑有限元方法使用任意n边多边形单元（CS-FEM-Poly）是为解决流体力学问题而开发的。采用基于特征的分裂与稳定压力梯度投影 (CBS/SPGP) 相结合的稳定方法来处理 CS-FEM-Poly 的数值振荡。我们验证了 CS-FEM-Poly，并在四个典型数值示例上使用三角形、四边形和多边形元素测试其数值行为。数值结果表明，基于 CBS/SPGP 的 CS-FEM-Poly 产生了与基准的精确解一致的解，并且与 FEM 相比，给出了理想的收敛速度。在后向阶梯流示例中，凹单元的数值鲁棒性在 CS-FEM-Poly 中得到体现。