In this paper, the exhaustive usage and implementation of Streamline-Upwind/Petrov-Galerkin method combining with Stabilized Pressure Gradient Projection (SUPG/SPGP) for incompressible Navier-Stokes equations are investigated. We validate and explore the behavior of cell-based smoothed finite element method (CS-FEM) and finite element method (FEM) based on SUPG/SPGP on five numerical examples. First, the Taylor-Green vortex example shows that CS-FEM based on SUPG/SPGP (CSFEM-SUPG/SPGP) are more accurate and has better robustness against distorted mesh than that of FEM based on SUPG/SPGP (FEM-SUPG/SPGP). Moreover, the wider range of SPGP stability parameter for CS-FEM-SUPG/SPGP is found in the condition of maintaining accurate result. Meanwhile, the lid-driven cavity flow example shows that the SUPG/SPGP method is favorable for incompressible flow at relatively high Reynolds number. The other numerical examples show good performances of the proposed method on the unsteady flows and micro-channel flow. In summary, proposed CS-FEM-SUPG/SPGP shows good performances on obtaining accurate results.

本文研究了不可逆Navier-Stokes方程的Streamline-Upwind / Petrov-Galerkin方法与稳定压力梯度投影（SUPG / SPGP）相结合的详尽用法和实现。我们在五个数值示例上验证并探索了基于单元的平滑有限元方法（CS-FEM）和基于SUPG / SPGP的有限元方法（FEM）的行为。首先，泰勒-格林涡流示例表明，与基于SUPG / SPGP（FEM-SUPG / SPGP）的FEM相比，基于SUPG / SPGP的CS-FEM（CSFEM-SUPG / SPGP）更准确，并且对扭曲网格具有更好的鲁棒性）。此外，在保持准确结果的条件下，发现CS-FEM-SUPG / SPGP的SPGP稳定性参数范围更广。与此同时，盖驱动腔流动的例子表明，SUPG / SPGP方法对于较高雷诺数下的不可压缩流动是有利的。其他数值算例表明了该方法在非定常流动和微通道流动方面的良好性能。总之，提出的CS-FEM-SUPG / SPGP在获得准确结果方面显示出良好的性能。