High-order mapped WENO methods with improved efficiency

This paper is devised to improve the efficiency of mapped WENO (WENO-M) methods. The WENO-M methods apply a mapping function on the nonlinear weights to recover the optimal accuracy at extremal points and meanwhile improve the resolution of numerical solutions at non-smooth regions. But this mapping process increases the computational costs as well. To improve the efficiency of WENO-M methods, we develop a simple mapping function which is applied on the indicators of smoothness (not on the nonlinear weights). The mapped indicators of smoothness are sufficient to obtain the optimal accuracy at extremal points. The computational costs are also deceased since the nonlinear weights are only required to be computed once in each WENO reconstruction. Finally, several numerical tests confirm that the improved WENO-M (WENO-IM) methods have the similar numerical accuracy with WENO-M methods, but less computational costs. (C) 2021 Elsevier Ltd. All rights reserved.