TY - JOUR
T1 - Development of a WENO scheme based on radial basis function with an improved convergence order
AU - Jeong, Byeongseon
AU - Yang, Hyoseon
AU - Yoon, Jungho
N1 - Funding Information:
J. Yoon was supported in part by the National Research Foundation of Korea under grant NRF-2020R1A2C1A01005894 . B. Jeong was supported by the Bisa Research Grant of Keimyung University in 2021. H. Yang was supported by the National Research Foundation of Korea grant funded by the Korea government (MSIT) ( NRF-2022R1F1A1066389 ).
Publisher Copyright:
© 2022 Elsevier Inc.
PY - 2022/11/1
Y1 - 2022/11/1
N2 - 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.
AB - 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.
KW - Hyperbolic conservation laws
KW - Order of accuracy
KW - Radial basis function
KW - Shape parameter
KW - Smoothness indicator
KW - WENO scheme
UR - http://www.scopus.com/inward/record.url?scp=85135955299&partnerID=8YFLogxK
U2 - 10.1016/j.jcp.2022.111502
DO - 10.1016/j.jcp.2022.111502
M3 - Article
AN - SCOPUS:85135955299
VL - 468
JO - Journal of Computational Physics
JF - Journal of Computational Physics
SN - 0021-9991
M1 - 111502
ER -