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

In this article, we introduce a class of fifth-order WENO schemes based on Newton interpolation polynomial, termed WENO-NIP schemes. We develop a class of smoothness indicators that measure the local smoothness of a function in a stencil, which are based on L-1-norm. Compared with the classical WENO-JS scheme, the WENO-NIP scheme has more succinct form, and can provide the fifth convergence order in smooth regions, even at critical points where the first and second derivatives vanish (but the third derivatives are non-zero). Numerical results demonstrate that the new scheme achieves excellent performance in resolving complex flow features. Compared with the WENO-JS scheme and the WENO-NS scheme, the WENO-NIP scheme provides improved behavior for practical shock capturing problems. (C) 2019 Elsevier Ltd. All rights reserved.