New simple local smoothness indicators for fifth-order WENO schemes simulating compressible flows

For the WENO-Z scheme, the structure of the local smoothness indicators has a significant impact on the computational performance of the weighted essentially non-oscillatory scheme with a given global smoothness indicator. In this paper, a new class of two-parameter local smoothness indicators is constructed by combining the classical fifth-order WENO-JS and WENO-UD5 schemes and locally appending the coefficients of the higher-order terms of the new local smoothness indicators. A new WENO scheme, WENO-NSLI, is constructed using the global smoothness indicators of WENO-UD5. Numerical experiments show that the new scheme can achieve optimal accuracy at the critical point when the parameter (lambda,mu) = (0.5, 10) is taken and has a higher resolution than WENO-JS, WENO-Z, and WENO-UD5.

Automated summary

This paper investigates the impact of the structure of local smoothness indicators on the computational performance of the WENO-Z scheme. A new class of two-parameter local smoothness indicators is proposed, which combines the classical WENO-JS and WENO-UD5 schemes and appends the coefficients of higher-order terms. A new WENO scheme, WENO-NSLI, is constructed using the global smoothness indicators of WENO-UD5. Numerical experiments show that the new scheme achieves optimal accuracy and has higher resolution compared to WENO-JS, WENO-Z, and WENO-UD5.