多维SUPG格式不可压流动高精度算法研究

在传统流线迎风Petrov-Galerkin (SUPG)有限元法基础上，通过对稳定因子关键参数进行分析，提出了基于流向投影的最优特征高度参数确定方法，同时针对不可压流动引入变量分裂算法，发展了一种可用于高雷诺数不可压流动计算的高精度稳定化SUPG方法．详细地给出了三角形单元基于流向的最优特征高度确定方法的分析过程，并给出了基于分裂算法的有限元计算步骤和公式．采用该方法对典型的方腔拖曳、圆柱绕流流动问题进行了分析，在网格较稀疏，且雷诺数较大的情况下，依然可以得到稳定的计算结果，从而验证了该方法的稳定性、有效性，对实际工程应用具有积极的意义．

Study on the High-Precision Algorithm of Incompressible Flows With Multidimensional Streamline Upwind Petrov-Galerkin Format

Based on traditional streamline upwind Petrov-Galerkin (SUPG) FEM, by analyzing the key parameters of the stability factor, a new way for calculating the optimal characteristic height parameter through flow-direction-based projection (FDBP) is proposed. By introducing variable splitting algorithm, a high-precision SUPG algorithm with triangular element for incompressible flows with high Reynolds number is developed. The analysis process of the FDBP is given, as well as details of the finite element calculation steps and formula. Problems of lid-driven cavity flow and flow past a circular cylinder are analyzed by FDBP, the stable results can be obtained in the case of sparse grid and high Reynolds number, which proves its stability, accuracy and applicability.