A new global smoothness indicator of WENO scheme for hyperbolic conservation laws

In this paper, we propose a novel improved fifth-order WENO-Z scheme, referred to as the WENO-ZT scheme. This scheme is specifically designed to achieve and maintain fifth-order accuracy, even in the presence of critical points. By incorporating the high-order information from the classical WENO-Z scheme, we develop a new global smoothness indicator to evaluate the local smoothness of the function across the stencil, while simultaneously reducing computational cost. The performance of the proposed WENO-ZT scheme is evaluated through several test cases, including the linear advection equation and one-dimensional and two-dimensional compressible Euler equations. Both theoretical analysis and numerical experiments confirm that, compared to the WENO-JS, WENO-M, and WENO-Z schemes, the WENO-ZT scheme exhibits superior capability in resolving complex flow structures, achieving fifth-order accuracy, and reducing numerical dissipation.