An improved weighted essentially non-oscillatory scheme with modified smoothness indicator τ and adaptive index p

Abstract

The resolution and robustness properties of a numerical scheme are two mutually restricted aspects for the detailed simulation of complex flows. In the present paper, an improved seventh-order finite difference weighted essentially non-oscillatory scheme (WENO-PR) is developed by distributing larger weights to the less smooth stencils. To meet the optimization requirements, the high-order smoothness indicator τ is modified by some constraints and a real-number index factor p is designed under the control of a wavenumber identifier. The results show that the modifications in the proposed scheme improve self-adaptation features in the smooth and discontinuous regions, which greatly balance the numerical resolution and robustness. Compared with the existing schemes such as WENO-Z and WENO-JS, the WENO-PR is more flexible, accurate and robust. Several one- and two-dimensional numerical tests are performed to confirm the high-resolution capability and the non-oscillatory property of the proposed scheme.