• 论文 •

### 求解双曲守恒律的紧-WENO杂交格式及RBF-FD间断检测方法

1. 中国海洋大学数学科学学院, 青岛 266100
• 收稿日期:2019-09-10 出版日期:2020-09-15 发布日期:2020-09-15
• 基金资助:

国家自然科学基金（11871443）资助.

Yang Yang, Don Wai Sun, Gao Zhen, Wang Bao-Shan. HYBRID COMPACT-WENO SCHEME WITH RBF-FD BASED DISCONTINUITY DETECTION METHOD FOR HYPERBOLIC CONSERVATION LAWS[J]. Journal of Numerical Methods and Computer Applications, 2020, 41(3): 232-245.

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

Yang Yang, Don Wai Sun, Gao Zhen, Wang Bao-Shan

1. School of Mathematical Sciences, Ocean University of China, Qingdao 266100, China
• Received:2019-09-10 Online:2020-09-15 Published:2020-09-15

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.

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