Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5776141 | Journal of Computational and Applied Mathematics | 2018 | 32 Pages |
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 Ïθ 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 βÌk 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
Related Topics
Physical Sciences and Engineering
Mathematics
Applied Mathematics
Authors
Chang-Yeol Jung, Thien Binh Nguyen,