A new adaptive weighted essentially non-oscillatory WENO-θ scheme for hyperbolic conservation laws

Chang Yeol Jung, Thien Binh Nguyen

Research output: Contribution to journalArticle

Abstract

A new adaptive weighted essentially non-oscillatory WENO-θ scheme in the context of finite difference is proposed. Depending on the smoothness of the large stencil used in the reconstruction of the numerical flux, a parameter θ is set adaptively to switch the scheme between a 5th-order upwind and 6th-order central discretization. A new indicator τθ measuring the smoothness of the large stencil is chosen among two candidates which are devised based on the possible highest-order variations of the reconstruction polynomials in L2 sense. In addition, a new set of smoothness indicators β̃k of the substencils is introduced. These are constructed in a central sense with respect to the Taylor expansions around the point xj. Numerical results show that the new scheme outperforms other comparing 6th-order WENO schemes in terms of improving the resolution at critical regions of nonsmooth problems as well as maintaining symmetry in the solutions.

LanguageEnglish
Pages314-339
Number of pages26
JournalJournal of Computational and Applied Mathematics
Volume328
DOIs
StatePublished - 15 Jan 2018

Keywords

  • Adaptive upwind-central schemes
  • Euler equations
  • Hyperbolic conservation laws
  • Shock-capturing methods
  • Smoothness indicators
  • Weighted essentially non-oscillatory (WENO) schemes

Cite this

@article{1b2d4adcfcc5496cb3aeb909f6bce1a1,
title = "A new adaptive weighted essentially non-oscillatory WENO-θ scheme for hyperbolic conservation laws",
abstract = "A new adaptive weighted essentially non-oscillatory WENO-θ scheme in the context of finite difference is proposed. Depending on the smoothness of the large stencil used in the reconstruction of the numerical flux, a parameter θ is set adaptively to switch the scheme between a 5th-order upwind and 6th-order central discretization. A new indicator τθ measuring the smoothness of the large stencil is chosen among two candidates which are devised based on the possible highest-order variations of the reconstruction polynomials in L2 sense. In addition, a new set of smoothness indicators β̃k of the substencils is introduced. These are constructed in a central sense with respect to the Taylor expansions around the point xj. Numerical results show that the new scheme outperforms other comparing 6th-order WENO schemes in terms of improving the resolution at critical regions of nonsmooth problems as well as maintaining symmetry in the solutions.",
keywords = "Adaptive upwind-central schemes, Euler equations, Hyperbolic conservation laws, Shock-capturing methods, Smoothness indicators, Weighted essentially non-oscillatory (WENO) schemes",
author = "Jung, {Chang Yeol} and Nguyen, {Thien Binh}",
year = "2018",
month = "1",
day = "15",
doi = "10.1016/j.cam.2017.07.019",
language = "English",
volume = "328",
pages = "314--339",
journal = "Journal of Computational and Applied Mathematics",
issn = "0377-0427",
publisher = "Elsevier",

}

A new adaptive weighted essentially non-oscillatory WENO-θ scheme for hyperbolic conservation laws. / Jung, Chang Yeol; Nguyen, Thien Binh.

In: Journal of Computational and Applied Mathematics, Vol. 328, 15.01.2018, p. 314-339.

Research output: Contribution to journalArticle

TY - JOUR

T1 - A new adaptive weighted essentially non-oscillatory WENO-θ scheme for hyperbolic conservation laws

AU - Jung,Chang Yeol

AU - Nguyen,Thien Binh

PY - 2018/1/15

Y1 - 2018/1/15

N2 - A new adaptive weighted essentially non-oscillatory WENO-θ scheme in the context of finite difference is proposed. Depending on the smoothness of the large stencil used in the reconstruction of the numerical flux, a parameter θ is set adaptively to switch the scheme between a 5th-order upwind and 6th-order central discretization. A new indicator τθ measuring the smoothness of the large stencil is chosen among two candidates which are devised based on the possible highest-order variations of the reconstruction polynomials in L2 sense. In addition, a new set of smoothness indicators β̃k of the substencils is introduced. These are constructed in a central sense with respect to the Taylor expansions around the point xj. Numerical results show that the new scheme outperforms other comparing 6th-order WENO schemes in terms of improving the resolution at critical regions of nonsmooth problems as well as maintaining symmetry in the solutions.

AB - A new adaptive weighted essentially non-oscillatory WENO-θ scheme in the context of finite difference is proposed. Depending on the smoothness of the large stencil used in the reconstruction of the numerical flux, a parameter θ is set adaptively to switch the scheme between a 5th-order upwind and 6th-order central discretization. A new indicator τθ measuring the smoothness of the large stencil is chosen among two candidates which are devised based on the possible highest-order variations of the reconstruction polynomials in L2 sense. In addition, a new set of smoothness indicators β̃k of the substencils is introduced. These are constructed in a central sense with respect to the Taylor expansions around the point xj. Numerical results show that the new scheme outperforms other comparing 6th-order WENO schemes in terms of improving the resolution at critical regions of nonsmooth problems as well as maintaining symmetry in the solutions.

KW - Adaptive upwind-central schemes

KW - Euler equations

KW - Hyperbolic conservation laws

KW - Shock-capturing methods

KW - Smoothness indicators

KW - Weighted essentially non-oscillatory (WENO) schemes

UR - http://www.scopus.com/inward/record.url?scp=85027997486&partnerID=8YFLogxK

U2 - 10.1016/j.cam.2017.07.019

DO - 10.1016/j.cam.2017.07.019

M3 - Article

VL - 328

SP - 314

EP - 339

JO - Journal of Computational and Applied Mathematics

T2 - Journal of Computational and Applied Mathematics

JF - Journal of Computational and Applied Mathematics

SN - 0377-0427

ER -