### 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 τ^{θ} 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 L^{2} sense. In addition, a new set of smoothness indicators β̃_{k} of the substencils is introduced. These are constructed in a central sense with respect to the Taylor expansions around the point x_{j}. 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.

Language | English |
---|---|

Pages | 314-339 |

Number of pages | 26 |

Journal | Journal of Computational and Applied Mathematics |

Volume | 328 |

DOIs | |

State | Published - 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

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*Journal of Computational and Applied Mathematics*, vol 328, pp. 314-339. DOI: 10.1016/j.cam.2017.07.019

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

Research output: Contribution to journal › Article

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 -