A Modified Adaptive Improved Mapped WENO Method

Abstract

We propose a new family of mapped WENO schemes by using several adaptive control functions and a smoothing approximation of the signum function. The proposed schemes admit an extensive permitted range of the parameters in the mapping functions. Consequently, they have the capacity to achieve optimal convergence rates, even near critical points. Particularly, the new schemes with fine-tuned parameters illustrates a significant advantage when solving problems with discontinuities. It produces numerical solutions with high resolution without generating spurious oscillations, especially for long output times.