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

A new adaptive weighted essentially non-oscillatory WENO-theta 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 theta is set adaptively to switch the scheme between a 5th-order upwind and 6th-order central discretization. A new indicator re 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 (beta) over tilde (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. (C) 2017 Elsevier B.V. All rights reserved.