An improved weighted essentially non-oscillatory scheme with a new smoothness indicator

Youngsoo Ha; Chang Ho Kim; Yeon Ju Lee; Jungho Yoon

doi:10.1016/j.jcp.2012.06.016

An improved weighted essentially non-oscillatory scheme with a new smoothness indicator

Youngsoo Ha, Chang Ho Kim, Yeon Ju Lee, Jungho Yoon

Department of Mathematics

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

147 Scopus citations

Abstract

In this paper, we present a new smoothness indicator that evaluates the local smoothness of a function inside of a stencil. The corresponding weighted essentially non-oscillatory (WENO) finite difference scheme can provide the fifth convergence order in smooth regions, especially at critical points where the first derivative vanishes (but the second derivatives are non-zero). We provide a detailed analysis to verify the fifth-order accuracy. Some numerical experiments are presented to demonstrate the performance of the proposed scheme. We see that the proposed WENO scheme provides at least the same or improved behavior over the fifth-order WENO-JS scheme [10] and other fifth-order WENO schemes called as WENO-M [9] and WENO-Z [2], but its advantage seems more salient in two dimensional problems.

Original language	English
Pages (from-to)	68-86
Number of pages	19
Journal	Journal of Computational Physics
Volume	232
Issue number	1
DOIs	https://doi.org/10.1016/j.jcp.2012.06.016
State	Published - 1 Jan 2013

Bibliographical note

Funding Information:
The authors are very grateful to the anonymous referee for the valuable suggestion on this paper. This work was supported by Basic Science Research Program 2010–0011689 (Y. Lee) and Priority Research Centers Program 2011–0022979 (Y. Lee, J. Yoon), through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology .

Keywords

Approximation order
Euler equation
Hyperbolic conservation laws
Smoothness indicator
WENO scheme

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10.1016/j.jcp.2012.06.016

Cite this

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title = "An improved weighted essentially non-oscillatory scheme with a new smoothness indicator",

abstract = "In this paper, we present a new smoothness indicator that evaluates the local smoothness of a function inside of a stencil. The corresponding weighted essentially non-oscillatory (WENO) finite difference scheme can provide the fifth convergence order in smooth regions, especially at critical points where the first derivative vanishes (but the second derivatives are non-zero). We provide a detailed analysis to verify the fifth-order accuracy. Some numerical experiments are presented to demonstrate the performance of the proposed scheme. We see that the proposed WENO scheme provides at least the same or improved behavior over the fifth-order WENO-JS scheme [10] and other fifth-order WENO schemes called as WENO-M [9] and WENO-Z [2], but its advantage seems more salient in two dimensional problems.",

keywords = "Approximation order, Euler equation, Hyperbolic conservation laws, Smoothness indicator, WENO scheme",

author = "Youngsoo Ha and {Ho Kim}, Chang and {Ju Lee}, Yeon and Jungho Yoon",

note = "Funding Information: The authors are very grateful to the anonymous referee for the valuable suggestion on this paper. This work was supported by Basic Science Research Program 2010–0011689 (Y. Lee) and Priority Research Centers Program 2011–0022979 (Y. Lee, J. Yoon), through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology .",

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AU - Ha, Youngsoo

AU - Ho Kim, Chang

AU - Ju Lee, Yeon

AU - Yoon, Jungho

N1 - Funding Information: The authors are very grateful to the anonymous referee for the valuable suggestion on this paper. This work was supported by Basic Science Research Program 2010–0011689 (Y. Lee) and Priority Research Centers Program 2011–0022979 (Y. Lee, J. Yoon), through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology .

PY - 2013/1/1

Y1 - 2013/1/1

N2 - In this paper, we present a new smoothness indicator that evaluates the local smoothness of a function inside of a stencil. The corresponding weighted essentially non-oscillatory (WENO) finite difference scheme can provide the fifth convergence order in smooth regions, especially at critical points where the first derivative vanishes (but the second derivatives are non-zero). We provide a detailed analysis to verify the fifth-order accuracy. Some numerical experiments are presented to demonstrate the performance of the proposed scheme. We see that the proposed WENO scheme provides at least the same or improved behavior over the fifth-order WENO-JS scheme [10] and other fifth-order WENO schemes called as WENO-M [9] and WENO-Z [2], but its advantage seems more salient in two dimensional problems.

AB - In this paper, we present a new smoothness indicator that evaluates the local smoothness of a function inside of a stencil. The corresponding weighted essentially non-oscillatory (WENO) finite difference scheme can provide the fifth convergence order in smooth regions, especially at critical points where the first derivative vanishes (but the second derivatives are non-zero). We provide a detailed analysis to verify the fifth-order accuracy. Some numerical experiments are presented to demonstrate the performance of the proposed scheme. We see that the proposed WENO scheme provides at least the same or improved behavior over the fifth-order WENO-JS scheme [10] and other fifth-order WENO schemes called as WENO-M [9] and WENO-Z [2], but its advantage seems more salient in two dimensional problems.

KW - Approximation order

KW - Euler equation

KW - Hyperbolic conservation laws

KW - Smoothness indicator

KW - WENO scheme

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JO - Journal of Computational Physics

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ER -

An improved weighted essentially non-oscillatory scheme with a new smoothness indicator

Abstract

Bibliographical note

Keywords

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