An improved WENO scheme with a new smoothness indicator

We present a new smoothness indicator that evaluates the local smoothness of a function inside of a stencil. The corresponding weighted essentially non-oscillatory (WENO) finite difference scheme can provide the fifth convergence order in smooth regions. The proposed WENO scheme provides at least the same or improved behavior over the classical fifth-order WENO scheme [9] and other fifth-order WENO schemes called as WENO-M [8] and WENO-Z [2], but its advantage seems more salient in two dimensional problems. Some numerical experiments are presented to demonstrate the performance of the proposed scheme.