New Constructing Method for WENO Schemes

A new method for constructing weighted essentially non-oscillatory (WENO) scheme is proposed. The idea of this method is to combine Henrick's mapping function and the idea of improving the accuracy of WENO-Z scheme one-by-one order. The particular advantage of the new constructing method is that it can improve the accuracy of WENO scheme near discontinuities. Numerical examples show that the new constructing method is very efficient and robust, and the new WENO scheme is more accurate than the original ones.