Development of a WENO scheme based on radial basis function with an improved convergence order
- 주제(키워드) Hyperbolic conservation laws , WENO scheme , Radial basis function , Shape parameter , Order of accuracy , Smoothness indicator
- 주제(기타) Computer Science, Interdisciplinary Applications; Physics, Mathematical
- 설명문(일반) [Jeong, Byeongseon] Keimyung Univ, Coll Nat Sci, Major Math, Daegu, South Korea; [Yang, Hyoseon] Kyung Hee Univ, Dept Math, Seoul 02447, South Korea; [Yoon, Jungho] Ewha Womans Univ, Dept Math, Seoul 03760, South Korea
- 관리정보기술 faculty
- 등재 SCIE, SCOPUS
- 발행기관 ACADEMIC PRESS INC ELSEVIER SCIENCE
- 발행년도 2022
- 총서유형 Journal
- URI http://www.dcollection.net/handler/ewha/000000203018
- 본문언어 영어
- Published As https://doi.org/10.1016/j.jcp.2022.111502
초록/요약
In this article, we present a novel RBF-WENO scheme improving the fifth-order WENO techniques for solving hyperbolic conservation laws. The numerical flux is implemented by incorporating radial basis function (RBF) interpolation to cell average data. To do this, the classical RBF interpolation is amended to be suitable for cell average data setting. With the aid of a locally fitting parameter in the RBF, the RBF-WENO reconstruction attains an additional one order of improvement, resulting in the sixth-order of accuracy. In addition, on the purpose of detecting small scale structures and steep gradients more accurately, we present new smoothness indicators by devising a method of generalized undivided differences with exponential vanishing moments. Several experimental results are performed to confirm the effectiveness of the proposed WENO method. (c) 2022 Elsevier Inc. All rights reserved.
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