基于简单分类方法的新型坏单元指示子  

A New Troubled-Cell Indicator for Discontinuous Galerkin Methods Using Simple Classification Method

作　　者：王之欢 赵郑豪 朱洪强[1] Wang Zhihuan;Zhao Zhenghao;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,江苏南京210023

出　　处：《宁夏大学学报（自然科学版）》2023年第3期201-206,共6页Journal of Ningxia University(Natural Science Edition)

基　　金：国家自然科学基金面上项目(11871443);江苏省研究生科研与实践创新计划项目(KYCX20-0787);南京邮电大学校级科研基金资助项目(NY222166)。

摘　　要：基于K均值聚类算法的坏单元指示子适用于各种指示变量和网格,且不含依赖于问题的参数,在数值测试中表现良好.新型坏单元指示子使用简单分类方法替换K均值聚类,不仅做法简单、易于数值实现,还不含对问题敏感的参数.对一维和二维经典算例的数值试验表明,新的坏单元指示子能精准捕捉间断,有效控制数值振荡,并显著节省计算时间.The troubled-cell indicator using K-means clustering can work with various indication variables and different grids.It is free of problem-dependent parameters and has good performance in the numerical tests.In this paper,we replace the K-means clustering with a simple classification method and obtain a simpler troubled-cell indicator that is easy to implement numerically and contains no problem-sensitive parameters.The numerical tests via one-dimensional and two-dimensional classical test problems demonstrate that the new troubled-cell indicator can detect the discontinuities accurately,control the numerical oscillations effectively and save the computational cost significantly.

关 键 词：坏单元指示子 限制器 Runge-Kutta间断Galerkin方法 双曲守恒律 

分 类 号：O241.82[理学—计算数学]