Novel weighted essentially non-oscillatory schemes with adaptive weights

摘要

In this paper, by constructing a selector that can identify the less-smooth sub-stencils, we have improved the classical WENO-JS and WENO-Z schemes, and developed two new WENO schemes which can adaptively increase the weight of less-smooth sub-stencils, WENO-IJS and WENO-IZ. Theoretical analysis shows that the present schemes maintain essentially non-oscillatory (ENO) property and have lower numerical dissipation at discontinuities. The investigation of approximate dispersion relation analysis (ADR) shows that the spectral characteristics of the present schemes are better than those of the classical WENO-JS, WENO-Z and WENO-Z+ schemes. A series of numerical experiments show that the shock wave capture capability and resolution of the complex process structure of the present schemes are significantly better than WENO-JS, WENO-Z and WENO-Z+.