### 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.

Original language | English |
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Pages (from-to) | 314-339 |

Number of pages | 26 |

Journal | Journal of Computational and Applied Mathematics |

Volume | 328 |

DOIs | |

Publication status | 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

*Journal of Computational and Applied Mathematics*,

*328*, 314-339. https://doi.org/10.1016/j.cam.2017.07.019