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 β ̃ 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.
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