A high-resolution WENO scheme with multiple global smoothness indicators in compressible fluids

A novel fifth-order WENO-Z-type scheme with multiple global smoothness indicators (MGSI-WENO-Z) is proposed for compressible multi-scale flows. Unlike conventional WENO-Z schemes with a single global smoothness indicator, distinct GSIs are assigned to individual sub-stencils: τ 0 = τ 2 = | β 0 + β 2 − 2 β 1 | for large-scale transitions and τ 1 = | β 0 − β 2 | for localized discontinuities. Nonlinear weights are constructed as α k = d k 1 + τ k β k + ϵ , enabling adaptive multiscale discrimination. Taylor analysis proves fifth-order accuracy in smooth regions and the ENO property near discontinuities. ADR analysis shows improved spectral resolution over WENO-Z5 and WENO-Z η 8-2. Extensive numerical experiments on benchmark problems including Sod’s, Shu–Osher, interacting blast waves, double Mach reflection, Kelvin–Helmholtz and Rayleigh–Taylor instabilities, and forward-facing step verify superior resolution and stability without non-physical oscillations.