Improved fifth-order weighted essentially non-oscillatory scheme with low dissipation and high resolution for compressible flows

Abstract

Compressible flows are numerically simulated using hyperbolic conservation laws. This study proposes a modified fifth-order weighted essentially non-oscillatory (WENO) scheme with a relatively low dissipation and high resolution for hyperbolic conservation laws. This scheme exhibits good performance when solving complex compressible flow fields containing strong discontinuities and smooth microstructures. A simple local smoothness indicator and an eighth-order global smoothness indicator are introduced to improve the accuracy. Furthermore, we construct a new optimal coefficient, which can be adaptively adjusted with different states of the flow field. It no longer depends on the grid spacing. This adaptive coefficient not only reduces dissipation while improving the resolution but also prevents negative dissipation and effectively suppresses spurious numerical oscillations. The proposed scheme attains a higher accuracy at high-order critical points than three classical WENO schemes. Moreover, analysis of the approximate dispersion relation indicates that the proposed scheme provides good dispersion and dissipation properties compared with other WENO schemes. Finally, several standard numerical experiments are performed to demonstrate the enhanced performance of the proposed scheme. The numerical results indicate that the present scheme has a low dissipation, high resolution, and good stability to capture both smooth and discontinuous structures.