In this paper, a characteristic‐based polynomial pressure projection (CBP3) scheme is proposed to stabilize finite element method for solving incompressible laminar flow. The characteristic‐Galerkin (CG) method is adopted as the stabilization for convection caused oscillation in CBP3 scheme. The pressure oscillation caused by incompressible constraint is stabilized by the polynomial pressure projection (P3) technique. Proposed scheme is suitable for any element using the equal‐order approximation for velocity and pressure. In this paper, the linear triangular and bilinear quadrilateral elements are adopted. The constant pressure projection is used for triangular elements. The CBP3 formulations for quadrilateral element are derived using both constant and linear pressure projections. Besides, the quasi‐implicit second‐order time stepping is adopted. The verification of CBP3 scheme implementation and validation of CBP3 scheme are accomplished by calculating several benchmarks. The results of CBP3 scheme reveal that the linear pressure projection for quadrilateral element is not appropriate due to its severe pressure oscillation. The well‐agreed results of CBP3 scheme using constant pressure projection demonstrate its good stabilization for FEM to solve both low and relatively high Reynolds number flows.

中文翻译：

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基于特征多项式压力投影方案的不可压缩流稳定有限元方法

本文提出了一种基于特征的多项式压力投影（CBP3）方案来稳定求解不可压缩层流的有限元方法。在CBP3方案中，采用特征加勒金（CG）方法作为对流引起的振荡的稳定化。由不可压缩约束引起的压力振荡通过多项式压力投影（P3）技术得以稳定。拟议的方案适用于对速度和压力采用等阶近似的任何元素。本文采用线性三角形和双线性四边形单元。恒压投影用于三角形元件。四边形单元的CBP3公式是使用恒定和线性压力投影得出的。此外，采用了准隐式二阶时间步长。通过计算几个基准来完成CBP3方案实现的验证和CBP3方案的验证。CBP3方案的结果表明，四边形单元的线性压力投影由于其剧烈的压力振荡而不合适。使用恒压投影的CBP3方案的公认结果表明，它对有限元法具有很好的稳定性，可以解决相对较低的雷诺数流量和​​相对较高的雷诺数流量。