An Efficient Adaptive Central-Upwind WENO-CU6 Numerical Scheme with a New Sensor

We present a novel efficient adaptive central-upwind WENO-CU6 scheme (named as EWENO-CU6) to maximize the order of accuracy, minimize dissipation and improve numerical robustness. Unlike WENO-CU6 scheme, the present paper introduces a switch formula based on our new shock sensor to adaptively diminish numerical dissipation in a rational manner when departing from discontinuities. Based on the above improvements, the performances of several schemes are characterized in scalar equations, which indicate new scheme’s high order of accuracy, robustness with a reasonable computational efficiency in wavenumber space. A variety of benchmark cases of Euler equations are tested to further verify the new scheme’s performance. From multi-dimensional tests, EWENO-CU6 scheme shows a greater resolving power in practical flow cases involving both shocks and complex features. We emphasize that this method can be applied more broadly for any algorithm which contains the similar reference smoothness indicator in WENO-CU class schemes.