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Jung, Chang-Yeol
Analysis and computational methods Lab
Research Interests
  • Analysis, singular perturbations, uncertainty, numerical methods

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

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Title
A new adaptive weighted essentially non-oscillatory WENO-θ scheme for hyperbolic conservation laws
Author
Jung, Chang-YeolNguyen, Thien Binh
Keywords
Hyperbolic conservation laws;  Euler equations;  Shock-capturing methods;  Weighted essentially non-oscillatory (WENO) schemes;  Adaptive upwind-central schemes;  Smoothness indicators
Issue Date
201801
Publisher
ELSEVIER SCIENCE BV
Citation
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, v.328, no., pp.314 - 339
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.
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DOI
http://dx.doi.org/10.1016/j.cam.2017.07.019
ISSN
0377-0427
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