The weighted ENO scheme based on the modified smoothness indicator

In this note, we try to improve the numerical resolution around the discontinuous region by simply modifying the original smoothness indicator in WENO-JS scheme [1]. The purpose of this modification is to slightly increase the weight of less-smooth stencil. The procedure of modification only increases about 1% of CPU time compared with the classical WENO-JS scheme. And the modified scheme generates comparable numerical solutions with the WENO-M scheme [2] (which increases about 25% in CPU cost).