A Modified Adaptive Improved Mapped WENO Method (Communications in Computational Physics, 2021)
We propose a new family of mapped WENO schemes by using several adaptive control functions and a smoothing approximation of the signum function. Theproposed schemes admit an extensive permitted range of the parameters in the mapping functions. Consequently, they have the capacity to achieve optimal convergencerates, even near critical points. Particularly, the new schemes with fine-tuned parameters illustrates a significant advantage when solving problems with discontinuities. Itproduces numerical solutions with high resolution without generating spurious oscillations, especially for long output times.