A new strategy for implementing mapped WENO method

The mapping is a useful technique for improving the performance of WENO method. However, for the existed mapped WENO methods, two weaknesses still need to be overcome. First, too much computational cost is used, the computational cost of mapped WENO method is around 43 of the original WENO method. Second, on the nonuniform meshes, too much memory space is used. We can take the WENO-RM method on nonuniform rectangle meshes for example, which is one of the famous mapped WENO methods. Comparing to original WENO method, the WENO-RM needs to store 128×M additional parameters, where M is the cell number. In order to overcome these weaknesses, we propose a new strategy for implementing the mapped WENO method. Different from the previous works, the new strategy is based on the average weight. The new strategy has following major advantages: first, it can give the solution which is as accurate as the original mapped WENO method; second, it can save the computational cost, because it only uses slightly more computational cost than the original WENO method; third, it can save the memory space because it only needs to store a little additional parameter compared to the original WENO method.