RKDG方法改进的K均值聚类坏单元指示子  

Improved troubled-cell indicator using K-means clustering for RKDG methods

作　　者：赵郑豪 王之欢 朱洪强[1] ZHAO Zhenghao;WANG Zhihuan;ZHU Hongqiang(School of Science,Nanjing University of Posts and Telecommunications,Nanjing 210023,China)

机构地区：[1]南京邮电大学理学院,南京210023

出　　处：《扬州大学学报（自然科学版）》2023年第2期6-11,18,共7页Journal of Yangzhou University：Natural Science Edition

基　　金：国家自然科学基金资助项目(11871443);江苏省研究生科研与实践创新计划资助项目(KYCX20_0787);南京邮电大学校级科研基金资助项目(NY222166)。

摘　　要：为解决K均值聚类坏单元指示子中双实数型可调参数给数值应用带来的不便,通过采用简单、高效的数据归一化和极差的方法,直接筛选出含有坏单元的模板,再使用K均值聚类筛选出坏单元,从而将双参数改为单参数.数值计算结果表明,改进的坏单元指示子不仅继承了原方法的优点,而且极大地降低了确定参数的复杂度,有利于该算法的实际应用.The K-means clustering based troubled-cell indicator contains two adjustable real parameters which brings inconvenience to numerical applications.To resolve this problem,the author first singles out the stencils which contain troubled cells via data normalization and range,and then singles out the troubled cells by K-means clustering.As a result,the number of parameters in the scheme is reduced from two to one.The numerical results show that the improved troubled-cell indicator not only inherits the advantages of the original method,but also greatly reduces the complexity of parameter determination,which is conductive to the practical application of the algorithm.

关 键 词：坏单元指示子 K均值聚类 Runge-Kutta间断Galerkin方法 

分 类 号：O241.7[理学—计算数学]