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A novel method for constructing robust and high-order accurate weightedessentially non-oscillatory (WENO) scheme is proposed in this paper. The methodis mainly based on the WENO-Z type scheme, in which, an eighth-order globalsmoothness indicator (the square of the approximation of the fourth-orderderivative on the five-point stencil used by the fifth-order WENO scheme) isused, and in order to keep the ENO property and robustness, the constant 1 usedto calculate the un-normalized weights is replaced by a function of localsmoothness indicators of candidate sub-stencils. This function is designed tohave following adaptive property: if the five-point stencil contains adiscontinuity, then the function approaches to a small value, otherwise, itapproaches to a large value. Analysis and numerical results show that theresulted WENO-Z type (WENO-ZN) scheme is robust for capturing shock waves and,in smooth regions, achieves fifth-order accuracy at first-order critical pointand fourth-order accuracy at second-order critical point.

A novel method for constructing high accurate and robust WENO-Z type scheme