Development of a WENO scheme based on radial basis function with an improved convergence order

Byeongseon Jeong; Hyoseon Yang; Jungho Yoon

doi:10.1016/j.jcp.2022.111502

Development of a WENO scheme based on radial basis function with an improved convergence order

Byeongseon Jeong, Hyoseon Yang, Jungho Yoon

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

9 Scopus citations

Abstract

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.

Original language	English
Article number	111502
Journal	Journal of Computational Physics
Volume	468
DOIs	https://doi.org/10.1016/j.jcp.2022.111502
State	Published - 1 Nov 2022

Bibliographical note

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.

Keywords

Hyperbolic conservation laws
Order of accuracy
Radial basis function
Shape parameter
Smoothness indicator
WENO scheme

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10.1016/j.jcp.2022.111502

Cite this

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title = "Development of a WENO scheme based on radial basis function with an improved convergence order",

abstract = "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.",

keywords = "Hyperbolic conservation laws, Order of accuracy, Radial basis function, Shape parameter, Smoothness indicator, WENO scheme",

author = "Byeongseon Jeong and Hyoseon Yang and Jungho Yoon",

note = "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: {\textcopyright} 2022 Elsevier Inc.",

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doi = "10.1016/j.jcp.2022.111502",

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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

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U2 - 10.1016/j.jcp.2022.111502

DO - 10.1016/j.jcp.2022.111502

M3 - Article

AN - SCOPUS:85135955299

SN - 0021-9991

VL - 468

JO - Journal of Computational Physics

JF - Journal of Computational Physics

M1 - 111502

ER -

Development of a WENO scheme based on radial basis function with an improved convergence order

Abstract

Bibliographical note

Keywords

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