Efficient WENOCU4 scheme with three different adaptive switches

Although classical WENOCU schemes can achieve high-order accuracy by introducing a moderate constant parameter C to increase the contribution of optimal weights, they exhibit distinct numerical dissipation in smooth regions. This study presents an extension of our previous research which confirmed that adaptively adjusting parameter C can indeed overcome the inadequacy of the usage of a constant small value. Cmin is applied near a discontinuity while Cmax is used elsewhere and they are switched according to the variation of the local flow-field property. This study provides the reference values of the adaptive parameter C of WENOCU4 and systematically evaluates the comprehensive performance of three different switches (labeled as the binary, continuous, and hyperbolic tangent switches, respectively) based on an optimized efficient WENOCU4 scheme (labeled as EWENOCU4). Varieties of 1D scalar equations, empirical dispersion relation analysis, and multi-dimensional benchmark cases of Euler equations are analyzed. Generally, the dissipation and dispersion properties of these three switches are similar. Especially, employing the binary switch, EWENOCU4 achieves the best comprehensive properties. Specifically, the binary switch can efficiently filter more misidentifications in smooth regions than others do, particularly for the cases of 1D scalar equations and Euler equations. Also, the computational efficiency of the binary switch is superior to that of the hyperbolic tangent switch. Moreover, the optimized scheme exhibits high-resolution spectral properties in the wavenumber space. Therefore, employing the binary switch is a more cost-effective improvement for schemes and is particularly suitable for the simulation of complex shock/turbulence interaction. This study provides useful guidance for the reference values of parameter C and the evaluation of adaptive switches.