A mapping-function-free WENO-M scheme with low computational cost

The classical WENO-JS scheme developed by Jiang and Shu [5] suffers accuracy loss near a critical point in smooth region. An extra mapping process was introduced by Henrick et al. [6] to overcome this problem with significantly increased computational cost, known as WENO-M scheme. In order to reduce the cost brought by the mapping process, a pre-discrete mapping method is proposed in this article. The cost of this new method is not only low, but also independent of the complexity of mapping function. Numerical experiments with one- and two- dimensional benchmark problems are conducted to demonstrate the effectiveness of this new method. Compared to the original method, the cost is reduced by 52%.