Steady-state two-dimensional lid-driven square cavity flows at high Reynolds numbers are solved in this communication using a velocity-based formulation developed in the context of the improved element-free Galerkin–reduced integration penalty method (IEFG–RIPM). The analyses based on the IEFG–RIPM are performed under a standard Galerkin weak-formulation, i.e. without the need of introducing streamline-upwind or pressure stabilizing terms in order to suppress the appearance of non-physical oscillations. Solutions in a wide range of high Reynolds numbers are successfully achieved, and the results obtained have exhibited an excellent agreement with mesh-based solutions reported in the literature. The numerical performance of the proposed IEFG–RIPM in the solution of such benchmark problem has been analysed in terms of velocity distribution, streamline patterns, vorticity and pressure contours, and also in terms of the properties of primary and secondary vortices. The outcomes of this study demonstrate the potential of the IEFG–RIPM as a feasible and reliable numerical technique for the analysis of lid-driven square cavity flows at high Reynolds numbers, allowing the fulfilment of accuracy and stability numerical requirements demanded in the solution of this benchmark problem in a remarkably simple manner.

在这种通信中，使用在改进的无元素伽辽金减少积分惩罚方法 (IEFG-RIPM) 的背景下开发的基于速度的公式，解决了高雷诺数下的稳态二维盖驱动方腔流动。基于IEFG-RIPM 的分析是在标准Galerkin 弱公式下进行的，即不需要引入流线逆风或压力稳定项来抑制非物理振荡的出现。成功实现了各种高雷诺数的解决方案，并且获得的结果与文献中报道的基于网格的解决方案非常吻合。已根据速度分布分析了所提出的 IEFG-RIPM 在解决此类基准问题时的数值性能，流线型、涡度和压力等值线，以及初级和次级涡流的特性。这项研究的结果证明了 IEFG-RIPM 作为一种可行且可靠的数值技术的潜力，用于分析高雷诺数下的盖驱动方腔流动，从而满足解决该问题所需的精度和稳定性数值要求。以非常简单的方式进行基准测试。