A Cell-Based Smoothed Finite Element Method for Arbitrary Polygonal Element to Solve Incompressible Laminar Flow

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.