Compressible flows typically exhibit multiple shock waves which interact with each other, making the detection of these shock waves crucial for various aspects of flow studies including construction of high-order numerical schemes (e.g., shock-fitting), adaptive grid refinement, and flow visualization. This study aims to effectively identify and localize multiple shock waves and their interaction points in two-dimensional inviscid steady and unsteady flows. A novel shock wave pattern recognition method based on cluster analysis is proposed, including three processes. First, a series of grid-cells located at the transition zones of captured shock waves are extracted using a shock wave detection approach based on local flow variation. Subsequently, these grid-cells are grouped into numerous clusters using the classical -means clustering algorithm, with categorization based on nearest neighbor features. Finally, a strategy is introduced to merge relevant adjacent clusters and further localize the points where shock waves interact. The Bézier curve fitting technique is then employed to obtain the high-quality shock-lines. Several numerical cases demonstrate that this method achieves high localization accuracy for shock-lines while being minimally affected by grid type and scale variations. Moreover, it enables clear and effective identification of the shock interaction patterns in both steady and unsteady flows, providing an effective visualization means for analyzing the motion and evolution of shock wave configurations.

中文翻译：

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基于聚类分析的二维无粘可压缩流激波模式识别方法

可压缩流通常表现出多个相互作用的冲击波，使得这些冲击波的检测对于流动研究的各个方面至关重要，包括构建高阶数值方案（例如，冲击拟合）、自适应网格细化和流动可视化。本研究旨在有效识别和定位二维非粘性稳态和非稳态流中的多个冲击波及其相互作用点。提出了一种基于聚类分析的冲击波模式识别新方法，包括三个过程。首先，使用基于局部流量变化的冲击波检测方法提取位于捕获的冲击波过渡区域的一系列网格单元。随后，使用经典的均值聚类算法将这些网格单元分组为许多簇，并根据最近邻特征进行分类。最后，引入一种策略来合并相关的相邻簇并进一步定位冲击波相互作用的点。然后采用贝塞尔曲线拟合技术来获得高质量的冲击线。多个数值案例表明，该方法可以实现冲击线的高定位精度，同时受网格类型和尺度变化的影响最小。此外，它能够清晰有效地识别稳态和非稳态流中的冲击相互作用模式，为分析冲击波构型的运动和演化提供有效的可视化手段。