一种基于聚类分析的二维激波模式识别算法

在激波捕捉求解器计算的可压缩无黏流场基础上，提出了一种探测并识别二维激波干扰模式的新算法，从3个层面详细介绍了该算法的实施流程。首先，采用基于当地流场参数设计的传统激波探测方法，辨识出激波附近的一系列网格单元；其次，通过经典的K-means聚类算法将这些激波单元划分成许多簇，并根据簇的相邻信息定义每个簇的类别；最后，设定相关准则对某些紧邻的簇进行合并，进而确定各个激波干扰点的位置，记录各条激波分支所对应的簇，采用Bézier曲线拟合算法分别对其聚类中心进行拟合以获取更加光滑的激波线。数值试验表明，该算法不受网格类型的限制，不仅可以保证最终拟合的激波线具有较高的位置精度，还可以清晰地识别出流场中多激波干扰的模式，同时对分析非定常流场中激波的运动与演化过程也提供了一种有效的可视化手段。

A two-dimensional shock wave pattern recognition algorithm based on cluster analysis

Based on compressible and inviscid flow solutions computed by shock-capturing solvers, a new technique for detecting and recognizing two-dimensional shock wave interaction patterns is proposed. The implementation process of this algorithm is illustrated from three aspects. Firstly, using a traditional shock wave detection approach based on local flow parameters, a series of grid-cells near the shock waves are identified. Next, the shock cells are divided into various clusters by means of a classical K-means clustering algorithm, and the category of each cluster is defined according to its adjacent information. Finally, a criterion is introduced to merge related adjacent clusters and to further determine the locations of shock interaction points. The clusters contained in each shock wave are recorded, and then all the fitting shock lines can be obtained by the Bézier curve algorithm. Numerical experiments show that this newly developed technique can be used in different types of mesh, The new technique produces fitted shock lines with high quality and positional accuracy. Meanwhile, the multiple shock wave interaction patterns are clearly recognized and provide a good visualization method for analyzing the motion and evolution of shock waves in complex, unsteady flow.