An improved WENO-Z scheme for accurate shock wave capturing

Shock waves are one of the common features in explosive shock flow fields, and accurately capturing shock waves in the flow field is crucial for achieving high-precision numerical simulations of explosive shock problems. In this paper, based on the classic Weighted Essentially Non-oscillatory (WENO) scheme, a new fifth-order WENO scheme with higher resolution and lower dissipation is proposed by introducing a local smoothness indicator with a more concise form and a global smoothness indicator that includes information from all sub-templates. The new scheme possesses the Essentially Non-oscillatory (ENO) property and maintains fifth-order convergence accuracy at the zeroth-order and first-order critical points. Accuracy tests and results from typical numerical examples demonstrate that the new scheme improves resolution and reduces dissipation compared with traditional WENO schemes (WENO-JS and WENO-Z). The improvements enable more precise shock wave capturing and propagation characterization, ultimately advancing high-accuracy numerical simulation of explosion and impact dynamics.