Improvement of the WENO scheme smoothness estimator

Abstract

This paper has analyzed the weights of the fifth-order weighted essentially nonoscillatory scheme suggested by Jiang and Shu and a modified smoothness estimator is suggested to improve the accuracy. Using a function of the minimum and maximum of the original smoothness estimators, the new smoothness estimators have smaller variation among them than the original ones in smooth regions. Hence, as the new weights are closer to the optimal weights, the numerical accuracy is improved. Several numerical experiments are presented to demonstrate the accuracy and robustness of the new scheme. © 2009 John Wiley & Sons, Ltd.