求解双曲守恒律的紧-WENO杂交格式及RBF-FD间断检测方法  

HYBRID COMPACT-WENO SCHEME WITH RBF-FD BASED DISCONTINUITY DETECTION METHOD FOR HYPERBOLIC CONSERVATION LAWS

作　　者：杨洋 曾维新 高振 王保山 Yang Yang;Don Wai;Sun Gao;Zhen Wang;Bao-Shan(School of Mathematical Sciences,Ocean University of China,Qingdao 266100,China)

机构地区：[1]中国海洋大学数学科学学院,青岛266100

出　　处：《数值计算与计算机应用》2020年第3期232-245,共14页Journal on Numerical Methods and Computer Applications

基　　金：国家自然科学基金(11871443)资助.

摘　　要：设计准确、鲁棒和高效的间断检测方法,在任意给定的网格单元和任意时间上衡量解的光滑度,是杂交格式的关键问题.本文从有限差分形式的径向基函数(RBF-FD)方法出发设计间断检测方法,为解决其阈值参数的选取问题,采用数据分析中Tukey’s箱线图方法增强算法的鲁棒性,最终提出一种准确、鲁棒和高效的RBF-FD间断检测方法.数值结果分析表明,RBF-FD间断检测方法在间断捕捉的准确性、鲁棒性和效率等方面优于已有的RBF方法和单调多项式插值方法,并且与五阶WENO-Z格式相比,应用RBF-FD方法的杂交格式可以加速2倍左右.An accurate,robust and efficient discontinuity detection method to detect the smoothness of solutions at any given grid point and time,is the key problem of hybrid schemes.By using finite difference radial basis function(RBF-FD) method and increasing the robustness of the discontinuity detection method by employing the Tukey’s boxplot method in data analysis,an accurate,robust and efficient RBF-FD based discontinuity detection method is proposed.Several classical benchmark examples show that the RBF-FD method captures shocks better than the original RBF discontinuity detection method and the monotone interpolation method in terms of accuracy,robustness,and efficiency.The hybrid scheme with the proposed RBF-FD method is about two times more efficient in the CPU times than the fifth order WENO-Z scheme.

关 键 词：间断检测方法 RBF-FD WENO格式 杂交格式 

分 类 号：O241.82[理学—计算数学]