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

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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 (λ,μ)=(0.5,10) is taken and has a higher resolution than WENO-JS, WENO-Z, and WENO-UD5.